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Geometry Angle Bisectors Problem

Source:

August 11, 2019
geometryangle bisectorcircumcircle

Problem Statement

Let ABCABC be a triangle and let Ω\Omega be its circumcircle. The internal bisectors of angles A,BA, B and CC intersect Ω\Omega at A1,B1A_1, B_1 and C1C_1, respectively, and the internal bisectors of angles A1,B1A_1, B_1 and C1C_1 of the triangles A1A2A3A_1 A_2 A_ 3 intersect Ω\Omega at A2,B2A_2, B_2 and C2C_2, respectively. If the smallest angle of the triangle ABCABC is 40∘40^{\circ}, what is the magnitude of the smallest angle of the triangle A2B2C2A_2 B_2 C_2 in degrees?
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