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A circle inscribed in a quadrilateral

Source: Romanian IMO TST 2006, day 3, problem 1

May 16, 2006
geometryincentertrigonometryconicshyperbolaromania

Problem Statement

The circle of center II is inscribed in the convex quadrilateral ABCDABCD. Let MM and NN be points on the segments AIAI and CICI, respectively, such that ∠MBN=12∠ABC\angle MBN = \frac 12 \angle ABC. Prove that ∠MDN=12∠ADC\angle MDN = \frac 12 \angle ADC.
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