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Notes 68: (10.5) Apply Other Angle Relationships in Circles

Notes 68: (10.5) Apply Other Angle Relationships in Circles. THEOREM10.11. 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. m  1 = AB m  1 = ACB.

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Notes 68: (10.5) Apply Other Angle Relationships in Circles

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  1. Notes 68: (10.5) Apply Other Angle Relationships in Circles

  2. THEOREM10.11 • 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. • m1 = AB • m1 = ACB

  3. THEOREM 10.12: ANGLES INSIDE THE CIRCLE THEOREM • 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. • m1 = (m AB + m CD) • m2 = (m AD + m BC)

  4. THEOREM 10.13: ANGLES OUTSIDE THE CIRCLE THEOREM • If a tangent and a secant, two tangents, or two secants intersect outsidea circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs. m1 = (m BC – m AC) m2 = (m PQR – m PR) m1 = (m BC – m AC)

  5. Find angle and arc measures • Line m is tangent to the circle. Find the indicated measure. m1 m EFD

  6. Find an angle measure inside a circle • Find the value of x.

  7. Find an angle measure outside a circle • Find the value of x.

  8. Independent Practice #1 • m ACB

  9. Independent Practice #2 • Find x.

  10. Independent Practice #3 • Find y.

  11. Independent Practice #4 • Find a.

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