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Prove the fraction on cotangents

Source:

October 7, 2010

trigonometrygeometry unsolvedgeometry

Problem Statement

Let

ABCD

be a convex quadrilateral whose diagonals

AC

and

BD

intersect in a point

P

. Prove that

\frac{AP}{PC}=\frac{\cot \angle BAC + \cot \angle DAC}{\cot \angle BCA + \cot \angle DCA}