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Olympiad proof problem

There is a convex quadrilateral ABCD and it's diagonals intersect at P . PE,PF,PG and PH are the altitudes from point P to sides AB,BC,CD and DA respectively.Prove that this quadrilateral will have an incircle only if 1/ PE + 1/PG = 1/PF + 1/ PH .

Note by Raven Herd
1 year, 9 months ago

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