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Tangential quadrilaterals

Source: 2020 Turkey TST P2

March 14, 2020
geometryperimeter

Problem Statement

A1A2A3A4A_1A_2A_3A_4 is a tangential quadrilateral with perimeter p1p_1 and sum of the diagonals k1k_1 .B1B2B3B4B_1B_2B_3B_4 is a tangential quadrilateral with perimeter p2p_2 and sum of the diagonals k2k_2 .Prove that A1A2A3A4A_1A_2A_3A_4 and B1B2B3B4B_1B_2B_3B_4 are congruent squares if p12+p22=(k1+k2)2 p_1^2+p_2^2=(k_1+k_2)^2
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