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Warm-up #5 A B C D 63 o ( 9x o Find x and m AD

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Table of Contents Section 41. 10.4 Other Angle Relationships in Circles

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10.4 Other Angle Relationships in Circles Essential Question – How can you use the angles formed by secants and tangents to solve problems?

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Tangent and chord intersection If a tangent & a chord intersect at a pt. on a circle, then the measure of each formed is ½ the measure of its intercepted arc. m 1 = ½ m AB m 2 = ½ m BCA ( ( A B C 1 2

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Example: Find m 1 = m 2 = m BCA = ( A B C 12 150 o 75 o 105 o 210 o

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Chord intersection When 2 chords intersect, the measure of each angle is ½ the sum of the measures of the arcs intercepted by the angle & its vertical angle. A B C D 1 m 1 = ½ (m AB + m DC) ((

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Example: Find x. 40 o 120 o xoxoxoxo ½ (40 + 120) ½ (160) = 80 o 80 o x = 180 - 80 x = 100 o

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Tangent and secant intersection When tangents and secants intersect, the measure of the angle formed is ½ the difference of the measures of the intercepted arcs. There are 3 cases for this thm. Case 1: A B C X m X = ½ (m BC – m AC) ((

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Case 2:Case 3: A B C X m X = ½ (m ACB – m AB) ( ( A B C D Y m Y = ½ (m BC – m AD) ((

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Example: Find x. xoxoxoxo 80 o x = ½ (280 – 80) x = ½ (200) x = 100 o xoxoxoxo 78 o 204 o 78 = ½ (204 – x) 156 = 204 – x - 48 = - x x = 48 o 280 o 360 – 80 = 280 o

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Assignment Pg. 624: 9-33 odd

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Assessment Pair and share

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SECANTS Secant - A line that intersects the circle at two points.

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