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<I_1DI_2 = 90^o for incenters of ABP, ACP, D touchpoint of incircle with BC

Source: 2020 1st OMpD L2 P4 - Brazil - Olimpíada Matemáticos por Diversão

September 23, 2022
geometryincenterright triangleright angle

Problem Statement

Let ABCABC be a triangle and PP be any point on the side BCBC. Let I1I_1,I2I_2 be the incenters of triangles ABPABP and ACPACP, respectively. If DD is the point of tangency of the incircle of ABCABC with the side BCBC, prove that ∠I1DI2=90o\angle I_1DI_2 = 90^o.
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