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incenter wanted, 1/AE + 1/AF =( a + b + c)/ bc.

Source: 2007 Moldova JBMO TST 1.3

July 12, 2020
geometryincenter

Problem Statement

Let ABCABC be a triangle with BC=a,AC=bBC = a, AC = b and AB=cAB = c. A point PP inside the triangle has the property that for any line passing through PP and intersects the lines ABAB and ACAC in the distinct points EE and FF we have the relation 1AE+1AF=a+b+cbc\frac{1}{AE} +\frac{1}{AF} =\frac{a + b + c}{bc}. Prove that the point PP is the center of the circle inscribed in the triangle ABCABC.
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