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Easy geo with tangent circles

Source: Kvant Magazine No. 4 M2554

March 14, 2023
geometryKvant

Problem Statement

Two externally tangent circles Ω1\Omega_1 and Ω2\Omega_2 are internally tangent to the circle Ω\Omega at AA and BB, respectively. If the line ABAB intersects Ω1\Omega_1 again at DD and C∈Ω1∩Ω2C\in\Omega_1\cap\Omega_2, show that ∠BCD=90∘\angle BCD=90^\circ.
Proposed by V. Rastorguev
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