Download - Maths P2 MP1

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Half-Yearly Examinations - Maths Paper-II

Model Paper-I

Part-A

Time: 2 Hours Maximum Marks: 35

Section-I

Group-A

(Geometry, Analytical Geometry, Statistics)

1. Prove that the tangents at the ends of a diameter of a circle are parallel.

2. Find the point on x–axis which is equidistant from (2,3) and (4,–2)

3. Find the equation of straight line passing through the points (4,–7) and (1,5)

4. Write the merits of Arithmetic Mean?

Group-B

(Matrices, Computing)

5. Show that AB ≠ 0, BA=0, If..

6. A matrix D has an inverse. D–1= Find D.

7. Write the characteristics of a computer.

8. Define the i) Algorithem ii) Flow chart

Section-II

9. Find the distance between the centres of two cicles whose radii are 5 cm and 7 cm having

three common tangents?

3 41 2

⎡ ⎤⎢ ⎥⎣ ⎦

1 0B =

0⎡ ⎤⎢ ⎥⎣ ⎦a

0 0A =

1 0⎡ ⎤⎢ ⎥⎣ ⎦

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11. Find the median of the following observations 1.8, 4.0, 2.7, 1.2 , 4.5, 2.3, 3.1 and 3.7 .

12. Maximise the objective function at (0,120) and (80, 40).

13. One end of the diameter of a circle is (2,3) and the centgre is (–2,5). Find the co-ordinate

of the other end of the diameter.

14. Define programming language.

Section-III

Group-A

15. State and prove Pythagoras Theorem.

16. The point G(0,6) is the centroid of the triangle, two of whose vertices are A(–4,4), B(6,12)

Find the co-ordinates of the third vertex. Show that area of Δ ABC = 3(area of Δ AGB).

17. Find the area of the triangle enclosed between the coordinate axes and the line passing

through (8,–3) and (–4, 12).

18. Marks scored by 100 students in a 25 marks unit test of mathematics is given below. Find

the median.

Marks 0-5 5-10 10-15 15-20 20-25

Students 10 18 42 23 7

Group-B

(Matrices, Computing)

19. Given that and (A+B)2 = A2+B2. Find a,b.

20. Solve the following equations using matrix inversion method

1 1 a 1 A = ,B =

2 1 b 1−⎡ ⎤ ⎡ ⎤

⎢ ⎥ ⎢ ⎥− −⎣ ⎦ ⎣ ⎦

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21. What are the different boxes used in a flow chart? Describe their functions in details?

22. Write an algorithm and draw a flow chart to pick largest number of the three given number?

Section-IV

(Polynomials, Linear Programming)

23. Draw a circumcircle to a ABC with measures AB= 4 cm, BC= 4 cm, and AC= 6 cm.

24. Construct a triangle ABC in which BC= 5cm, A= √70° and median AD through A= 3.5cm.

PART-B

Marks : 30×½=5

1. ΔABC ∼ Δ DEF, m ∠A + m∠B = 130° then ∠f = –––––––––––. ( )

A) 130° B) 140° C) 50° D) 40°

2. The line y= mx+c intersect the x–axis at the point ––––––––. ( )

A) (0,C) B) (C,0) C) (–c/m, 0) D) (0, –c/m)

3. The slope of the line joining (4,6) and (2,–5) is ––––––––––– . ( )

A) 6/5 B) –2/4 C) 5/6 D) 11/2

4. The histogram consists of ––––––––––– . ( )

A) sectors B) triangles C) Squares D) rectangles

5. The median of the scores 13, 23, 12, 18, 26, 19 and ––––––––––– . ( )

A)14 B) 26 C) 13 D) 18

6. The arthmetic mean of a+2, a, a–2 is –––––––––––. ( )


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7. If and A= B then p and x are –––––––––––.( )

A) p= 6, x= 2 B) p=2, x=6 C) p=3, x=4 D) p=4, x=3

8. If then the order of AT is = –––––––––––. ( )

A) 3×2 B) 2×2 C) 2×3 D) 3×3

9. The father of computer –––––––––––. ( )

A) Pascal B) Bill gates C) Charles Babbage D) Newin

10. Vaccum tubes are used in –––––––– generation of computers. ( )

A) fourth B) First C) Second D) Third

Answers : 1. C 2. C 3. D 4. D 5. D

6. B 7. A 8. A 9. C 10. B

II. Fill in the blanks with suitable words. Marks : 10×½=5

11. Angle in a semi circle is –––––––.

12. Basic proportionality theorem is also known as ––––––––– theorem.

13. The slope of a line perpendicular to 2x+3y=4 is –––––––.

14. If A.M. of 3, 5, 9, x, 11 is 7 then x = –––––––.

15. Formula for calculation the median of frequency distribution is ———.

16. The angle between the lines x–2=0 and y+3=0 is ––––––––.

1 2 3A =

4 5 6⎡ ⎤⎢ ⎥⎣ ⎦

3 4 3 4 A = , B =

6 p 2⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦x


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18. , If A has not multiplicative inverse then x= ––––––––.

19., then AB = ––––––––.

20. Expand C.P.U. ––––––.

Answers

11. Right angle 12. Thales

13. 3/2 14. 7

15. x2+2x–15=0 16. 90

17. 45 18. √a + √b

19. 1/13 20. 4

III. Match the following. Marks : 10×½=5

Group-A Group-B

21. The height of the equilateral ( ) A) 2

triangle of side 2√3 is

22. If C= 90° in Δ ABC and

a =3, b=4, then C= ( ) B) y–y1 = m(x–x1)

23. Slope and point form of ( ) C) a

a line.

24. The equation of y-axis is ( ) D) 3a

25. A.M. of a–d, a, a+d is ( ) E) 3

[ ]5A , B x y

2⎡ ⎤

= =⎢ ⎥⎣ ⎦

4 xA

x 9⎡ ⎤

= ⎢ ⎥⎣ ⎦


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G)

H) –5

Answers : 21. E 22. F 23. B 24. A 25. C

Group-A Group-B

26. ( ) A) 1

27. ( ) B) 5

28. If = 0 then a = ( ) C) A–1.B–1

29. (AB)–1 ( ) D) ∝

30. Computer ( ) E) cos θ

F) B–1.A–1

G) sin θ

H) An electronic machine

Answers : 26. G 27. A 28. B 29. F 30. H

2a 56 3

2Tanπ

2sec 1sec

θ −θ

x y 1a b

+ =


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Key

Section-I

Group-A

1. Prove that the tangents at the ends of a diameter of a circle are parallel.

A. Given: Let 'O' be the centre of the circle and be a diameter. Let and be the two

tangents drawn at A and B to the circle with centre 'O'

R.T.P. //

Proof: ∠A = ∠B = 90° –1) (Tangent is perpendicular to the diameter at the point of contact)

Let and be two lines and be a transversal then A and ∠B = 90° + 90° = 180°

(since From 1)

If two lines are cut off a transversal and a pair of interior

angles So formed are supplementary then the two lines are

parallel.

//

2. Find the point on x-axis which is equidistant from (2,3) and (4,–2)?

A. Let the required point be (x,0)

Distance between (x,0) and (2,3) = Distance between (x,0) and (4,–2)

2x 8x 16 4= − + +2x 4x 4 9⇒ − + +

2(x 4) 4= − +2(x 2) 9⇒ − +

2(x 4) 4= − +2(x 2) 9⇒ − +

2 2(x 4) 0 ( 2)= − + − −2 2(x 2) (03)∴ − +

BDAC

ABBDAC

BDAC

BDACAB


B D

CA

O

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x2–4x+13 = x2–8x+20

⇒ –4x+13+8x–20 = 0 ⇒ 4x–7 = 0

x = 7/4 ∴ The required point is (7/4, 0)

3. Find the equation of straight line passing through the points (4,–7) and (1,5)

A. Equation of a line passing through two points is

4. Write the merits of Arithmetic mean?

A. Merits of Arithmetic mean:

i) It is uniquely defined

ii) It is based on all observations

iii) It is easily understood

iv) It is easy to compute

Group-B

5. Show that AB ≠≠ 0, BA=0, If..

A.

∴ AB ≠ 0, BA=0

1 0 0 0 0 0 0 0 0 0BA 0

0 0 1 0 0 0 0 0 0 0+ +⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎛ ⎞

= = = =⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟+ +⎝ ⎠⎝ ⎠ ⎝ ⎠ ⎝ ⎠0 0 1 0 0 0 0 0

AB1 0 0 0 1 0 0 0

+ +⎛ ⎞⎛ ⎞ ⎛ ⎞= =⎜ ⎟⎜ ⎟ ⎜ ⎟+ +⎝ ⎠⎝ ⎠ ⎝ ⎠

0 0 1 0A , B

1 0 0 0⎡ ⎤ ⎡ ⎤

= =⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

1 0B =

0⎡ ⎤⎢ ⎥⎣ ⎦a

0 0A =

1 0⎡ ⎤⎢ ⎥⎣ ⎦

4x y 9 0⇒ + − −y 7 4 x 16⇒ + = − −

y 7 4(x 4)⇒ + = − −12y 7⇒ + =

4

3−(x 4)−

5 ( 7)y 7 (x 4)1 4− −⇒ + = −

−12

1 12 1

y yy y (x x )

x x−

⇒ − = −−


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6. A matrix D has an inverse. D–1= Find D?

A. Let D= D–1= D. D–1 = I

2(3a+b=1) ––––1) 2(3c+d= 0) ––––3)

4a+2b=0 ––––––2) 4c+2d = 1 ––––– 4)

substitute a=1 in eq-1) substitute c= 1/2 in eq (3)

s(1) + b= 1 3(1/2) +d=0

b= 1–3 = –2 d= –3/2

∴ D= =

7. Write the characteristics of a computer?

A. Characteristics of a computer-

i) A computer can perform only those operation which are identified and concieved by a

human being.

1 -21/ 2 -3 / 2

⎡ ⎤⎢ ⎥⎣ ⎦

a bc d

⎡ ⎤⎢ ⎥⎣ ⎦

6c + 2d = 0

4c + 2d = 1- - -

2c = 1 c = 1/ 2

6a + 2b = 2

4a + 2b = 0- - -

2a = 2 a = 1

1 0

0 1⎡ ⎤

= ⎢ ⎥⎣ ⎦

3a + b 4a 2b

3c d 4c 2d+⎡ ⎤

⇒ ⎢ ⎥+ +⎣ ⎦

1 0a b 3 4 0 1c d 1 3

⎡ ⎤ ⎡ ⎤ ⎡ ⎤⇒ =⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦

3 41 2

⎡ ⎤⎢ ⎥⎣ ⎦

a bc d

⎡ ⎤⎢ ⎥⎣ ⎦

3 41 2

⎡ ⎤⎢ ⎥⎣ ⎦


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iii) It can perform various logical operations.

iv) It can perform million of computations and compile the result in a desired form in a few

minutes

8. Define the i) Algorithem ii) Flow chart

A. Algotithm: An algorithm is a disign or a plan of obtaining a solution to a problem. It forms

the central concept of the branch of computer science or informatics.

Flow chart: A diagramatic or a pictoral representation of the sequence of steps for solving

a problem is called flow chart.

Section-II

9. Find the distance between the centres of two cicles whose radii are 5 cm and 7 cm

having three common tangents?

A. If two circles have 3 common tangents, then they touch externally

d= r1+r2 = 5+7 = 12 cms.

10. Find the equation of the line passing through the point (–5,7) and slope is 4.

A. The given point (x1, y1) = (–5,7)

The given slope m = 4

Equation of the line having slope m and passing through the point (x1, y1) is

y–y1 = m(x–x1)

⇒ y–7 = 4(x–(–5)) ⇒ y–7 = 4(x+5)

⇒ y–7 = 4x+20


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11. Find the median of the following observations 1.8, 4.0, 2.7, 1.2, 4.5, 2.3, 3.1 and 3.7

A. The given observations are 1.8, 4.0, 2.7, 1.2, 4.5, 2.3, 3.1 and 3.7

The ascending order of the given observations is

1.2, 1.8, 2.3, 2.7, 3.1 3.7, 4.0, 4.5

Here, the no. of terms = 8

∴ 4th and 5th terms are the middle terms

∴ Average of the middle terms is the median

∴ Median =

12. If show that p is its own inverse?

A.

13. One end of the diameter of a circle is (2,3) and the centgre is (–2,5). Find the co-

ordinate of the other end of the diameter.

A. Given that one end of the diameter = (2,3)

Let the other end of the diamter = (x,y)

Center of the circle = (–2,5)

1 4P

0 1⎡ ⎤

= =⎢ ⎥−⎣ ⎦

1 410 11− −⎡ ⎤

= ⎢ ⎥− ⎣ ⎦1 1 41P

0 11 1 4 0− − −⎡ ⎤

= ⎢ ⎥× − × ⎣ ⎦

1 d b1Pc aad bc

− −⎡ ⎤= ⎢ ⎥−− ⎣ ⎦

1 4P

0 1⎡ ⎤

= ⎢ ⎥−⎣ ⎦

⎡ ⎤⎢ ⎥⎣ ⎦

1 4P =

0 -1

2.7 3.1 5.8 2.92 2+ = =


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2+x = –4 y= 10–3

x= –6 y= 7

∴ (–6,7) is other end of the diameter.

14. Define Programming Language?

A. Programming Language: Express the algorithm in a language understandable by a

computer. Such language is called programming language.

Section-III

Group-A

15. State and prove Pythagoras Theorem.

A. pythagoras theorem: In a right triangle, the square of the hypotenuse is equal to the sum

of the squares of the other two sides.

Given: In the triangle A,B.C, right angle is at B

To prove : AC2 = AB2 + BC2

Construction: BD⊥AC

proof: In Δles ADB and ABC.

∠A = ∠A (common)

∠ADB = ∠ABC = 90°

3 x 52+ =2 x 2

2+ = −

2 x 3 y, ( 2,5)2 2+ +⎛ ⎞ = −⎜ ⎟⎝ ⎠

1 2 1 2x x y y, ( 2,5)2 2+ +⎛ ⎞ = −⎜ ⎟⎝ ⎠


A

D

CB

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∴Δ ADB ∼ Δ ABC (A.A. similarity)

( In similar triangle corresponding sides are proportional)

AB2 = AD. AC ––––––– 1)

BC2 = DC. AC ––––––– 2)

Adding 1 and 2, we get

AB2+ BC2 = AD.AC+DC.AC = AC (AB+DC)

= AC. (AC) = AC2

∴ AC2 = AB2 + BC2

16. The point G(0,6) is the centroid of the triangle, two of whose vertices are A(–4,4),

B(6,12). Find the co-ordinates of the third vertex. Show that area of ΔΔ ABC = 3 (area

of ΔΔ AGB).

A. That area of ABC = 3(area of AGB)

Given that two vertices of a triangle are A (–4,4), B(6,12) and centroid is (0.6)

Let the third vertex is C(x,y), (6,12)

∴ centroid =

2+x = 0 16+y= 18

x= –2 y= 18–16= 2

16 y 63+ =

2 x 03+∴ =

2 x 16 y(0,6) ,3 3+ +⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

4 6 x 4 12 y(0,6) ,3 3

− + + + +⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

1 2 3 1 2 3x x x y y y,3 3

+ + + +⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

AD ABAB AC

∴ =


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Area of the Δ ABC

`

Area of Δ ABC = 18 sq. units ––––––– 1)

A (–4,4), G(0,6), B(6,12)

Area of Δ AGB

Area of Δ AGB = 6 sq.units ––––––– 2)

Area of Δ ABC = 3×Δ AGB sq.units

17. Find the area of the triangle enclosed between the coordinate axes and the line passing

through (8,–3) and (–4, 12).

A. The given points are (8,–3) and (–4,12)

Equation of the line passing through the given points is

⇒ 4(y+3) = –5(x–8) ⇒ 4y+12 = –5x + 40

⇒ 5x+4y+12–40 = 0 ⇒ 5x+4y–28 = 0

5x+4y= 28

153y −+ =5

412( )8x −

( ) ( )3 12y 3 x 88 ( 4)− −− − = −− −

( )2 11 1

2 1

y - yy - y = x - xx - x

1 122

= ×

1 24 122

= −1 4( 6) 0 6( 2)2

= − − + + −

1 4(6 12) 0(12 4) 6(4 6)2

= − − + − + −

1 36 18sq.units2

= × =1 362

= −

1 40 12 162

= − − +1 4(10) 6( 12) 2( 8)2

= − + − − −

1 2 3 2 3 1 3 1 21 x (y y ) x (y y ) x (y y )2

= − + − + −


O28/5,0

B

(0, 7)

A

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Y-intercept (b) = 7

∴ Area of the triangle enclosed between the coordinate axes is

18. Marks scored by 100 students in a 25 marks unit test of mathematics is given below.

Find the median.

A.

This is in the class 10–15

N 100N = 100 = 502 2

⇒ =

196 19.6 sq.units10

= =1 28 72 5

= ×

1 a b2

= ×

285

x y 128 7⇒ + =

x y 128 28⇒ + =

5x 4y 128 28

⇒ + =5x 4y 28 128 28+⇒ = =


Marks 0-5 5-10 10-15 15-20 20-25No. of students 10 18 42 23 7

Class Interval Frequency Cummulative Frequency

fi

0-5 10 105-10 18 28 = F10-15 = L 42 = f 7015- 20 23 9320-25 7 100

N = 100

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∴ L = 10, F= 28 , f = 42 and C= 5

= 10+ 2.619 = 12.62

∴ Median = 12.62.

19. Given that and (A+B)2 = A2+B2 Find a and b?

A. Given

––––––– 1)

––––––– 2)

∴ (A+B)2= A2+B2

2a b a 1ab b b

⎡ ⎤+ −= ⎢ ⎥−⎣ ⎦

2 a 1 a 1B = B B

b 1 b 1⎡ ⎤ ⎡ ⎤

× +⎢ ⎥ ⎢ ⎥− −⎣ ⎦ ⎣ ⎦

1 2 1 1 -1 0

2 2 2 1 0 1− − +⎡ ⎤ ⎡ ⎤

= =⎢ ⎥ ⎢ ⎥− − + −⎣ ⎦ ⎣ ⎦2 1 1 1 1

A = A A 2 1 2 1

− −⎡ ⎤ ⎡ ⎤× +⎢ ⎥ ⎢ ⎥− −⎣ ⎦ ⎣ ⎦

( )21+ a 0 0 0(2 + b)(1+ a) 0 4

⎡ ⎤+ +⎢ ⎥

+⎢ ⎥⎣ ⎦

( )2 1 a 0 01 aA + B = 2 b 2 22 b

+⎡ ⎤ ⎡ ⎤+⎡ ⎤+⎢ ⎥ ⎢ ⎥⎢ ⎥+ − −+⎣ ⎦⎣ ⎦ ⎣ ⎦

1 a 1 1 1+ a 0

2 b 1 1 2 + b 2+ − +⎡ ⎤ ⎡ ⎤

+⎢ ⎥ ⎢ ⎥+ − + −⎣ ⎦ ⎣ ⎦

1 1 a 1A + B =

2 1 b 1−⎡ ⎤ ⎡ ⎤

+⎢ ⎥ ⎢ ⎥− −⎣ ⎦ ⎣ ⎦

1 1 a 1 A = ,B =

2 1 b 1−⎡ ⎤ ⎡ ⎤

⎢ ⎥ ⎢ ⎥− −⎣ ⎦ ⎣ ⎦

⎡ ⎤⎢ ⎥⎣ ⎦

a 1B =

b -1⎡ ⎤⎢ ⎥⎣ ⎦

1 -1A =

2 -1

110= 10 +42

22 5= 10 +42×50 - 28= 10 + 5

42×

N F2 Median L + C

f

⎛ ⎞−⎜ ⎟∴ ×⎜ ⎟

⎜ ⎟⎝ ⎠


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a–1 = 0 b= 2

a= 1 a=1, b=4

20. Solve the following equations using matrix inversion method 2x+ 5y–11=0 and

4x–3y–9=0.

A. The given equations can be writen as 2x+5y = 11 –––––1)

and 4x–3y = 9 –––––– 2)

Expressing 1, 2, in the matrix equation form

We have

This is in the form of AX= B

Where

AX= B⇒ X= A–1.B

-3 -526 26-4 226 26

=

⎡ ⎤⎢ ⎥− −⎢ ⎥⎢ ⎥⎢ ⎥− −⎣ ⎦

-3 -51-4 2-6 - 20

= ⎡ ⎤⎢ ⎥⎣ ⎦

-3 -51-4 22x -3-5 4

= ⎡ ⎤⎢ ⎥× ⎣ ⎦

1 d -b1-c aad - bc

A =− ⎡ ⎤⎢ ⎥⎣ ⎦

11b

9⎡ ⎤

= ⎢ ⎥⎣ ⎦

xy

x ⎡ ⎤= ⎢ ⎥

⎣ ⎦

2 54 -3

A = ⎡ ⎤⎢ ⎥⎣ ⎦

119

⎡ ⎤= ⎢ ⎥

⎣ ⎦

xy

⎡ ⎤⎢ ⎥⎣ ⎦

2 54 -3

⎡ ⎤⎢ ⎥⎣ ⎦

( )( )

2 2a b -1 11 a 0 ab - b b2 b (1 a) 4

a⎡ ⎤ ⎡ ⎤+ −−= =⎢ ⎥ ⎢ ⎥+ +⎢ ⎥ ⎣ ⎦⎣ ⎦


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∴ X= A-1.B

∴ x=3, y= 1

21. What are the different boxes used in a flow chart? Describe their functions in details?

A. The following boxes are used in a flow chart.

22. Write an algorithm and draw a flow chart to pick largest number of the three given

numbers?

A. Algotithm

1) Read the three numbers labelled as A, B, C.

x 3y 1

⎡ ⎤ ⎡ ⎤=⎢ ⎥ ⎢ ⎥

⎣ ⎦ ⎣ ⎦∴

32 45 78326 26 26

44 -18 26 126 26 26

=

⎡ ⎤ ⎡ ⎤+⎢ ⎥ ⎢ ⎥ ⎡ ⎤= =⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎢ ⎥ ⎢ ⎥+⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

-

=

3−

511262694 -2

26 26

⎡ ⎤⎢ ⎥ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎣ ⎦⎢ ⎥⎣ ⎦


S.No Symbol Name of the Box Functions

1. Terminal Box It denotes both start/stop.

2. Data Box or To indicate the data fedInput, Output box into the computer and

print out given by the computer.

3. Operation Box To indicate any set of processing operationslike arithmetic operationsassignment etc.,

4. Decision Box To indicate the step of decision making.

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2) Compare A with B. If A is larger than B. Then compare A with C.

3) If A is again larger than C, then A is the largest of the three given numbers.

4) Other wise C is the largest number.

5) If in Step 2, If B is found larger than A, Compare B with C.

Section-IV

23. Draw a circumcircle to a Δ ABC with measures AB= 4 cm, BC= 4cm and AC= 6cm

A. Construction

i) Draw the triangle ABC with AB= 4cm

AC= 6cm. Say AB abd AC of the triangle and let these intersect at

a point O.

ii) Draw perpendicular bisectors of any triangle and let these intersect at a point O.

iii) Draw the circle with O as centre and radius R= OA= OB= OC.

iv) This is the required circumcircle of Δ ABC .


Read a,b,c

Print A Print C Print B

IsA>B

IsA>C

IsB>C

Start

Yes

Yes No

No No Yes

Stop Stop Stop

A 14cm

4 cm

B

CO

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24. Construct a triangle ABC in which BC= 5cm, ∠∠A = 70°, and median AD through A=

3.5 cm.

A. Construction

i) Draw a line segment BC= 5 cm and make the ∠CBP = 70°

ii) Draw . Also draw the perpendicular bisector of BC intersecting the ray BE in

and BC in D.

iii) Draw a circle taking O as centre and OB as radius.

iv) Taking B as centre and 3.5 cm as radius draw arcs intersecting the abopve drawn circle

in A, A1. Join AB abd AC and A'B, A'C. Either of the triabgles ABC, A'BC is the required

triangle.

proof: ∠PBC = ∠BAC = ∠BA'C = 70°

( Alternate segment theorem)

BC = 5cm, A'D= AD= 3.5 cm

∵

EB BP⊥


A

70°O

B

P

CD

A

E

70° 5cm

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Download - Maths P2 MP1

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