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Proof in a triangle

Source: Cono Sur 1992-problem 5

May 29, 2006
trigonometrygeometrycircumcirclegeometry unsolved

Problem Statement

In a △ABC\triangle {ABC}, consider a point EE in BCBC such that AE⊥BCAE \perp BC. Prove that AE=bc2rAE=\frac{bc}{2r}, where rr is the radio of the circle circumscripte, b=ACb=AC and c=ABc=AB.
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