Parts of a Circle Circle – set of all points _________ from a given point called the _____ of the circle (in a plane). equidistant C center Symbol: C

CHORD: a segment whose ________ are on the circle endpoints

RADIUS: distance from the _____ to a point on the circle center P

DIAMETER: distance ______ the circle through its ______ across P center Also known as the longest chord.

What is the relationship between the diameter and the radius of a circle? OR D = ½ D 2 r

D = ? 24 32 12 r = ? 16 r = ? 4.5 6 D = ? 12 9

Use P to determine whether each statement is true or false. Q R T S

SECANT sounds like second Secant Line A secant line intersects the circle at exactly TWO points. SECANT sounds like second

TANGENT: a LINE that intersects the circle exactly ONE time

Point of Tangency

Secant Radius Diameter Chord Tangent Name the term that best describes the line. Secant Radius Diameter Chord Tangent

Two circles can intersect… in two points one point or no points

No points of intersection (different center)

No points of intersection (same center) Concentric Circles Same center but different radii

1 point of intersection (Tangent Circles) Externally Tangent Internally Tangent

2 points of intersection

A point is inside a circle if its distance from the center is less than the radius. INTERIOR 

EXTERIOR  A point is outside a circle if its distance from the center is greater than the radius.

A point is on a circle if its distance from the center is equal to the radius. 

More Pythagorean Theorem type problems! Yeah!!  Point of Tangency More Pythagorean Theorem type problems! Yeah!!  If a line (segment or ray) is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

1. Find x A 12 B 9 a2 + b2 = c2 x 92 + 122 = x2 x = 15

RQ = 16 2. Find RQ a2 + b2 = c2 P 12 8 R Q 122 + (QR)2 = (8+12)2

r = 10 r2 + 242 = (r + 16)2 3. Find the radius. 16 A C 24 B

S If two segments from the same exterior point are tangent to a circle, then they are congruent. R T Party hat problems!

4. Find x R S T

5. Find x C A B

6. Find x. B A C P D E

7. Find NP N T S P R Q