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Geometry Problem 1132: Triangle, Excircle, Tangency Point, Parallel, Midpoint. Level: High School, SAT Prep, Honors Geometry, College, Math Education

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In a triangle ABC (figure below), the excircle E corresponding to BC is tangent to AB, BC, and AC at C1, A1, and B1, respectively. AB2 is parallel to A1B1 (B2 on C1A1 extended), AC2 is parallel to C1A (C2 on B1A1 extended). B2C2 intersects AC and AB at B3 and C3, respectively. Prove that B3C3 = BC/2.
 

Infographic Geometry problem 1132 Triangle, Excircle, Tangency Point, Parallel, Midpoint
 

 

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Last updated: Jul 11, 2015 by Antonio Gutierrez.