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Part of 2013 Balkan MO

Problems(1)

Excircles

Source: Balkan MO 2013, Problem 1

6/30/2013
In a triangle ABCABC, the excircle ωa\omega_a opposite AA touches ABAB at PP and ACAC at QQ, while the excircle ωb\omega_b opposite BB touches BABA at MM and BCBC at NN. Let KK be the projection of CC onto MNMN and let LL be the projection of CC onto PQPQ. Show that the quadrilateral MKLPMKLP is cyclic.
(Bulgaria)
geometryincentertrigonometryperimetercircumcircleHi