MathDB
congruent triangles wanted, starting with intersecting circles

Source: Indonesia INAMO Shortlist 2010 G3

August 27, 2021
geometrycongruent trianglescircles

Problem Statement

Suppose L1L_1 is a circle with center OO, and L2L_2 is a circle with center O′O'. The circles intersect at A A and B B such that ∠OAO′=90o\angle OAO' = 90^o. Suppose that point XX lies on the circumcircle of triangle OABOAB, but lies inside L2L_2. Let the extension of OXOX intersect L1L_1 at YY and ZZ. Let the extension of O′XO'X intersect L2L_2 at WW and VV . Prove that △XWZ\vartriangle XWZ is congruent with △XYV\vartriangle XYV.
Back to ProblemsView on AoPS