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Point Equidistant From Diagonals of a Rhombus

Source: Ukrainian Mathematical Olympiad 2023. Day 1, Problem 8.4

April 5, 2023
geometryrhombustangency

Problem Statement

Point TT is chosen in the plane of a rhombus ABCDABCD so that ∠ATC+∠BTD=180∘\angle ATC + \angle BTD = 180^\circ, and circumcircles of triangles ATCATC and BTDBTD are tangent to each other. Show that TT is equidistant from diagonals of ABCDABCD.
Proposed by Fedir Yudin
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