LET ABC BE AN ACUTE TRIANGLE WITH AB=C, BC=A, CA=B. IF D IS A POI...

3.

Let ABC be an acute triangle with AB=c, BC=a, CA=b. If D is a point on the side BC,

E and F are the foot of perpendicular from D to the sides AB and AC respectively.

Lines BF and CE meet at point P. If AP is perpendicular to BC, find the length of BD

in terms of

a b c , and prove that your answer is correct.

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