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10.4 Other Angle Relationships in Circles

# 10.4 Other Angle Relationships in Circles - 10.4 Other ∠...

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Unformatted text preview: 10.4 Other ∠ Relationships in Circles in p. 621 Thm 10.12 Thm If a tangent & a chord intersect at a pt. on a If circle, then the measure of each ∠ formed is ½ the measure of its intercepted arc. the B 1 A2 C m∠ 1 = ½ m AB m∠ 2 = ½ m BCA (( (( Example: Example Find m∠ 1 = m∠ 2 = m BCA = ( ( A 12 B C Thm 10.13 Thm If 2 chords intersect in the interior of a circle, If then the measure of each ∠ is ½ the sum of the measures of the arcs intercepted by the ∠ & its vertical ∠ . B A 1 D C m∠ 1 = ½ (m AB + m DC) ( ( ( ( Example: Find x. Example ½ (40 + 120) x = 180 - 80 If a tangent & a secant, 2 tangents or 2 If secants intersect in the exterior of a circle, then the measure of the ∠ formed is ½ the difference of the measures of the intercepted arcs. intercepted There are 3 cases for this thm. There cases Case 1: A X C m∠ X = ½ (m BC – m AC) B Thm 10.14 Thm ( ( ( ( Case 2: Case A X B C Y Case 3: A D C B m∠ X = ½ (m ACB – m AB) m∠ Y = ½ (m BC – m AD) ( ( ( ( ( ( ( ( Example: Find x. Example x = ½ (280 – 80) x = ½ (200) 78 = ½ (204 – x) 156 = 204 – x 156 - 48 = - x Assignment Assignment ...
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