Unit 7 Circles Parts of a Circle J

Unit 7 - Circles Parts of a Circle J Radius: distance from the center to a point on the circle 2 circles are if they have the same radius Diameter: is twice the radius PR R Chord: a segment whose endpoints are on the circle. v radius P Q S PR & PS are chords K Tangent: a line that intersects the circle in exactly 1 point. Ex. Line K Secant: a line that intersects a circle in two points. Ex. Line J

Circles can intersect in: One Point Two points No points Concentric Circles

Point of Tangency A line is tangent if it is perpendicular to the radius from the point of tangency. Point of tangency b a r c Use the Pythagorean Theorem to prove that the line is tangent… 2 a + b 2 = c 2 …or to find missing sides

Examples of point of tangency 1) Is EF tangent to circle D? 61 F D 60 11 612 = 112 + 602 3721 = 3721 Therefore EF is tangent because it forms a right angle and EF is perpendicular to DE E 2) B is the point of tangency. Find the radius. (r + 8)2 = r 2 + 162 r 2 + 16 r + 64 = r 2 + 256 16 r = 192 r = 12 16 B r A C 8 r

From a point (S) on the exterior, you can draw two tangents. So if RS & TS are tangent to the same outside point, then RS & TS are CONGRUENT!!! R S Find the value of x. C x 2 + 2 T A 11 B x 2 + 2 = 11 x 2 = 9 x = ± 3

Central Angles & Arcs Central Angle: an angle whose vertex is the center A Minor Arc: an angle less than 180° ex. APB = AB P Major Arc: is ACB B C Minor Arc = measure of the central angle Major Arc = 360 – minor arc

Find the measure of each arc of circle R. a) MN = 80° R N b) MPN = 360 - 80° = 280° P 80° c) PMN = 180° M G 40° R 80° 110° H a) m GE = 40 + 80 = 120° b) m GEF = 120 + 110 = 230° c) m GF = 360 – 230 = 130° F E