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3 externally tangent circles , PA is diameter of circle \Omega_a wanted

Source: Nigerian Senior Mathematics Olympiad 2019 Round 2 problem 3

September 8, 2019
geometrytangent circlesdiameter

Problem Statement

Circles Ωa\Omega_a and Ωb\Omega_b are externally tangent at DD, circles Ωb\Omega_b and Ωc\Omega_c are externally tangent at EE, circles Ωa\Omega_a and Ωc\Omega_c are externally tangent at FF. Let PP be an arbitrary point on Ωa\Omega_a different from DD and FF. Extend PDPD to meet Ωb\Omega_b again at BB, extend BEBE to meet Ωc\Omega_c again at CC and extend CFCF to meet Ωa\Omega_a again at AA. Show that PAPA is a diameter of circle Ωa\Omega_a.
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