MathDB

11.7

Part of 2003 All-Russian Olympiad Regional Round

Problems(1)

AT and AT' symmetric wrt angle bisectors, 2 spheres, tetrahedron

Source: - All-Russian MO 2003 Regional (R4) 11.7

9/17/2024
Given a tetrahedron ABCD.ABCD. The sphere ω\omega inscribed in it touches the face ABCABC at point TT. Sphere ω′\omega' touches face ABCABC at point T′T' and extensions of faces ABDABD, BCDBCD, CADCAD. Prove that the lines ATAT and AT′AT' are symmetric wrt bisector of angle ∠BAC\angle BAC
geometryangle bisector3D geometryspheretetrahedron