MathDB

5

Part of 2015 India National Olympiad

Problems(1)

Inmo 2015

Source: inmo 2015 #5

2/1/2015
Let ABCDABCD be a convex quadrilateral.Let diagonals ACAC and BDBD intersect at PP. Let PE,PF,PGPE,PF,PG and PHPH are altitudes from PP on the side AB,BC,CDAB,BC,CD and DADA respectively. Show that ABCDABCD has a incircle if and only if 1PE+1PG=1PF+1PH.\frac{1}{PE}+\frac{1}{PG}=\frac{1}{PF}+\frac{1}{PH}.
geometrytrigonometryvectorparallelogramanalytic geometryquadraticsgeometry unsolved