The above diagram shows a sector of a circle, with centre O and a radius 6 cm. The length of the arc AB is 8 cm. Find(i) Ð AOB(ii) the area of the shaded segment.(ii) the area of the shaded segment (θ - sin θ) (1.333 - sin 1.333) (36)(1.333 – 0.927) 6.498 c
CHORDChord of a circle is a line segment whose ends lie on the circle.
GIVEN THE RADIUS AND CENTRAL ANGLE
Chord length = 2r sin
EXAMPLE 1
Chord length = 2r sin = 2(6) sin = 12 x sin 45 = 8.49 cm
GIVEN THE RADIUS AND DISTANCE TO CENTER
This is a simple application of Pythagoras' Theorem.
Chord length =
EXAMPLE 2
Find the chord of the circle where the radius measurement is about 8 cm that is 6 units from the middle.
Solution:Chord length = = = = = 10.58 cm
SEMICIRCLE
PERIMETER OF A SEMICIRCLE Remember that the perimeter is the
distance round the outside. A semicircle has two edges. One is half of a circumference and the other is a diameter
So, the formula for the perimeter of a semicircle is: Perimeter = πr + 2r
EXAMPLE (PERIMETER)
Perimeter = πr + 2r = (3.142)+ 8 = 20.56 cm
AREA OF A SEMICIRCLE
A semicircle is just half of a circle. To find the area of a semicircle we just take half of the area of a circle.
So, the formula for the area of a semicircle is: Area =