section 10.1 circles. 10.1 notes what is a circle? a circle is the set of all points in a plane...
TRANSCRIPT
Section 10.1 Circles
10.1 Notes
What is a CIRCLE?
A CIRCLE is the set of all points in a plane equidistant from a given point.
A
10.1 Notes
There are points ON, IN, and OUTSIDE the circle.
The points in the circle make up the INTERIOR of the circle.
A
10.1 Notes
There are points ON, IN, and OUTSIDE the circle.
The points outside the circle are EXTERIOR POINTS.
A
10.1 Notes
A chord of a circle is a segment with both endpoints ON the circle.
is a chord.A
B
C
BC
10.1 Notes
A diameter of a circle is a chord that passes through the center.
is a diameter.
E
D
A
DE
10.1 Notes
A radius of a circle is a segment with one endpoint at the center of the circle and the other endpoint on the circle.
and are radii.E
D
A
AEDA
10.1 Notes
All radii are congruent since all points on the circle are equidistant from the center of the circle.
10.1 Notes
Can you see a relationship between the radius and diameter of a circle?
D
A
E
A
E
10.1 Notes
A diameter of a circle is equal to two radii of the circle.
A radius of a circle is equal to half of a diameter of the circle.
d r
r = 12d
d=2r
10.1 Notes
Finding diameter given radius:
r=6
r=1.7cm
d=12
d=3.4cm
6d=2r
1.7 cm d=2r
10.1 Notes
Finding diameter given radius:
r=4ft
d=8ft
r= m
d= m
d=2r
d=2r
d=24
2 3
3
10.1 Notes
Find diameter given radius:
1.
2. r=12m
3. r=7ft
3.2 cm
d=6.4cm
d=24m
d=14ft
10.1 Notes
Finding radius given diameter:
1. 2.
A P
B
C
AB = 18 ftPC = ?PB = ?
AB = 20mAP = ?PC = ?
10.1 Notes
Finding radius given diameter:
1.
A P
B
C
AB = 20mAP = ?PC = ? r=
12d
d=AB=20m
r = 10m
10.1 Notes
Finding radius given diameter:
2.
A P
B
C
AB = 18 ftPC = ?PB = ?
r = 9ft
r=12d
d=AB=18ft
10.1 Notes
Finding radius given diameter:
d= cm
r= cm
d=9m
r=4.5m
r = 12d
r = 12d
4 8
2 8
10.1 Notes
Find radius given diameter:
1. AB=30in
PC=?
PC=15in
2. d=42ft
r=21ft
3. d=10cm
r=5cm
A
P
BC
10.1 Notes
Tangent: a line which intersects a circle at exactly one point.
Point of tangency: the point where the tangent intersects the circle.
point of tangency
10.1 Notes
A common tangent is a line that is tangent to two circles.
A common tangent can either be a common external tangent or a common internal tangent.
10.1 Notes
common external tangent
10.1 Notes
common internal tangent
10.1 Notes
common external tangent
10.1 Notes
common internal tangent
10.1 Notes
Secant: a line that intersects a circle at two points.
10.1 Terms to know• exterior points-points that lie outside a circle.
• interior points-points that lie inside a circle.
• chord- a segment whose endpoints are on the circle.
• diameter-a chord that passes through the center of a circle.
• radius-a segment with one endpoint at the center of the circle and the other endpoint on the circle.
• tangent-a line which intersects a circle at exactly one point.
• point of tangency-the point where the tangent intersects the circle.
• common external tangent-a line that is tangent to two circles and DOES NOT intersect the segment connecting the two centers.
• common internal tangent-a line tangent to two circles that DOES intersect the segment connecting the two centers.
• secant-a line that intersects a circle at two points.