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

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

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

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

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 T Find the value of x. A B C x x = 11 x 2 = 9 x = ±3

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

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