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M is the midpoint of the chord PQ of a circle. AB and CD are two other chords through M. PQ meets AD at X and BC at Y. Prove that MX =MY. This result is called the Butterfly Theorem. (Hint. Drop perpendiculars from X and Y to AB and CD. Find four pairs of similar triangles.) A P M D B

M is the midpoint of the chord PQ of a circle. AB and CD are two other chords through M. PQ meets AD at X and BC at Y. Prove that MX =MY. This result is called the Butterfly Theorem. (Hint. Drop perpendiculars from X and Y to AB and CD. Find four pairs of similar triangles.) A P M D B

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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2. M is the midpoint of the chord PQ of a circle. AB and CD are two other chords through M. PQ meets AD at X and BC at Y. Prove that MX =MY. This result is called the Butterfly Theorem. (Hint. Drop perpendiculars from X and Y to AB and CD. Find four pairs of similar triangles.) A P M D B
Transcribed Image Text:2. M is the midpoint of the chord PQ of a circle. AB and CD are two other chords through M. PQ meets AD at X and BC at Y. Prove that MX =MY. This result is called the Butterfly Theorem. (Hint. Drop perpendiculars from X and Y to AB and CD. Find four pairs of similar triangles.) A P M D B
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