Altitudes from p onto the sides

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Let ABCD be a convex quadrilateral. Let the diagonals AC and BD intersect in P. Let P E, P F, P G and P H be the altitudes from P onto the sides AB, BC, CD and DA respectively. Show that ABCD has an incircle if and only if1P E+1P G =1P F+1P H

Reference no: EM131080851

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