Angles formed by Tangents Secants Chords Tangent a

Angles formed by Tangents, Secants & Chords Tangent & a Chord B C AB is a chord A is a tangent 2 1 A m 1 = ½ m. AB m 2 = ½ m. ACB If a tangent & a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.

Line m is tangent to the circle: a) Find the measure of angle 1 b) Find the measure arc PSR m B 1 m P R 130° A 150° m 1 = ½(150°) 1 = 75° S m = ½ (arc) 130° = ½(m. PSR) 260° = m. PSR

Find the m CBD A 9 x + 20 C Angle = ½ (arc) 5 x = ½(9 x + 20) 10 x = 9 x + 20 5 x B x = 20 m CBD = 5(20) = 100° D

Finding Angles & Arcs Given TWO Chords A 2 D Two chords intersect in the interior of the circle. B 1 The measure of each angle is equal to ½ the sum of the arcs. C m 1 = ½(m. BC + m. AD) m 2 = ½(m. DC + m. AB) Ex) Find the measure of an angle formed by two chords. Q 174° P 106° x S R Find x. x = ½(106 + 174) x = ½ (280) x = 140°

Tangent & a Secant Two Tangents P B A 2 1 C Q R m 1 = ½(m. BC – m. AC) m 2 = ½(m. PQR – m. PR) Two Secants X W m 3 = ½(m. XY – m. WZ) 3 Z Y

Find the value of x. m = ½(difference of the arcs) 72° = ½(200 – x) 144 = 200 – x 72° -56 = -x 56 = x E F 200° x° D G M 92° L N Find the m. MLN 360° – 92° = 268° So the m. MLN = 268° x° P x = ½(m. MLN – m. MN) x = ½(268 – 92) x = ½(176) x = 88°