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(con)cyclic wanted, 2 circles internally tangent to a third one, tangents

Source: Mathley 2014.1 p7

August 19, 2020
Concycliccyclic quadrilateraltangent circlesTangentssummer programgeometry

Problem Statement

The circles γ\gamma and δ\delta are internally tangent to the circle ω\omega at AA and BB. From AA, draw two tangent lines ℓ1,ℓ2\ell_1, \ell_2 to δ\delta, . From BB draw two tangent lines t1,t2t_1, t_2 to γ\gamma . Let ℓ1\ell_1 intersect t1t_1 at XX and ℓ2\ell_2 intersect t2t_2 at YY . Prove that the quadrilateral AXBYAX BY is cyclic.
Nguyen Van Linh, High School of Natural Sciences, Hanoi National University
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