Problem 6 Let K be a circle with centre O and L a smaller circle with centre Q which intersects K at A and B. Let P be the point where the tangent to K through A meets the tangent to L through B. Extend PB to meet K for a second time at X and let PA meet L for a second time at Y. (a) Prove that triangles OAQ, X AB and ABY are similar. (b) Find a triangle which is similar to triangle OAB.

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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Problem 6
Let K be a circle with centre O and L a smaller circle with centre Q which
intersects K at A and B. Let P be the point where the tangent to K
through A meets the tangent to L through B. Extend PB to meet K for
a second time at X and let PA meet L for a second time at Y.
(a) Prove that triangles OAQ, X AB and ABY are similar.
(b) Find a triangle which is similar to triangle OAB.
Transcribed Image Text:Problem 6 Let K be a circle with centre O and L a smaller circle with centre Q which intersects K at A and B. Let P be the point where the tangent to K through A meets the tangent to L through B. Extend PB to meet K for a second time at X and let PA meet L for a second time at Y. (a) Prove that triangles OAQ, X AB and ABY are similar. (b) Find a triangle which is similar to triangle OAB.
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