Unformatted text preview: , [ A,B ] respectively. Consider L ∈ BC { B,C } , M ∈ CA { C,A } , N ∈ AB { A,B } such that AL, BM, CN are concurrent. If P, Q, R are midpoints of AL BM, CN, respectively prove that PA , QB , RC are concurrent. 2 5. Prove that in a triangle ABC the altitude through A, the median through B and the internal angle bisector through C are concurrent iﬀ sin A = cos B tan C . 1 It is suﬃcient to show that Y C Y A = ZB ZA ! 2 Observe that P, Q, R lie on the sides of the medial triangle A B C ....
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 Spring '11
 cemtezer
 Geometry, triangle, Broome County, New York, concurrent iﬀ sin

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