MathDB

2006.10.4

Part of Kyiv City MO Seniors 2003+ geometry

Problems(1)

ABC isosceles if MN // PQ, incircle (Kyiv City Olympiad 2006 10.4)

Source:

6/28/2020
A circle ω\omega is inscribed in the acute-angled triangle △ABC\vartriangle ABC, which touches the side BCBC at the point KK. On the lines ABAB and ACAC, the points PP and QQ, respectively, are chosen so that PK⊥ACPK \perp AC and QK⊥ABQK \perp AB. Denote by MM and NN the points of intersection of KPKP and KQKQ with the circle ω\omega. Prove that if MN∥PQMN \parallel PQ, then △ABC\vartriangle ABC is isosceles.
(S. Slobodyanyuk)
geometryisoscelesparallelincircle