MathDB
triangle of intersections of angle bisectors with circumcircle

Source: 1991 ITAMO p1

January 31, 2020
geometryangle bisectorcircumcircle

Problem Statement

For every triangle ABCABC inscribed in a circle Γ\Gamma , let A′,B′,C′A',B',C' be the intersections of the bisectors of the angles at A,B,CA,B,C with Γ\Gamma . Consider the triangle A′B′C′A'B'C' . (a) Do triangles A′B′C′A'B'C' go over all possible triangles inscribed in Γ\Gamma as △ABC\vartriangle ABC varies? If not, what are the constraints? (b) Prove that the angle bisectors of △ABC\vartriangle ABC are the altitudes of △A′,B′,C′\vartriangle A',B',C' .
Back to ProblemsView on AoPS