MathDB
Diameter configuration

Source: Kyiv City MO 2024 Round 2, Problem 10.3

February 4, 2024
circumcirclegeometry

Problem Statement

Let AHA,BHB,CHCAH_A, BH_B, CH_C be the altitudes of the triangle ABCABC. Points A1A_1 and C1C_1 are the projections of the point HBH_B onto the sides ABAB and BCBC, respectively. B1B_1 is the projection of BB onto HAHCH_AH_C. Prove that the diameter of the circumscribed circle of △A1B1C1\triangle A_1B_1C_1 is equal to BHBBH_B.
Proposed by Anton Trygub
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