6 5 Apply Other Angle Relationships Theorem 6

6. 5 Apply Other Angle Relationships Theorem 6. 13 If a tangent and 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. B C A

6. 5 Apply Other Angle Relationships Example 1 Find angle and arc measures Line m is tangent to the circle. Find the indicated measure. B m E D m A Solution F

6. 5 Apply Other Angle Relationships Checkpoint. Find the indicated measure. A B C

6. 5 Apply Other Angle Relationships Theorem 6. 14 If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle. D A B C

6. 5 Apply Other Angle Relationships Example 2 Find an angle measure inside a circle Find the value of x. Solution The chords FH and GJ intersect inside the circle. F G J H

6. 5 Apply Other Angle Relationships Checkpoint. Find the value of x. F J G H

6. 5 Apply Other Angle Relationships Theorem 6. 15 If a tangent and a secant, two tangents, or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs. B A X P W Q C R Z Y

6. 5 Apply Other Angle Relationships Example 3 Find an angle measure outside a circle J Find the value of x. Solution The tangent GF and the secant GJ intersect outside the circle. H G F

6. 5 Apply Other Angle Relationships Checkpoint. Find the value of y. G H F K J

6. 5 Apply Other Angle Relationships Pg. 225, 6. 5 #1 -23