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angle of feet of angle bisectors wanted if <B=120^o

Source: 2013 Croatia MO p7

August 5, 2020
geometryanglesangle bisectorAngle Bisectors

Problem Statement

In triangle ABCABC, the angle at vertex BB is 120o120^o. Let A1,B1,C1A_1, B_1, C_1 be points on the sides BC,CA,ABBC, CA, AB respectively such that AA1,BB1,CC1AA_1, BB_1, CC_1 are bisectors of the angles of triangle ABCABC. Determine the angle ∠A1B1C1\angle A_1B_1C_1.
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