MathDB
2017 T9: Many Tangent Circles

Source:

January 29, 2017
2017team

Problem Statement

Circles ω1\omega_1 and ω2\omega_2 are externally tangent to each other. Circle Ω\Omega is placed such that ω1\omega_1 is internally tangent to Ω\Omega at XX while ω2\omega_2 is internally tangent to Ω\Omega at YY. Line ℓ\ell is tangent to ω1\omega_1 at PP and ω2\omega_2 at QQ and furthermore intersects Ω\Omega at points AA and BB with AP<AQAP<AQ. Suppose that AP=2AP=2, PQ=4PQ=4, and QB=3QB=3. Compute the length of line segment XY‾\overline{XY}.
Back to ProblemsView on AoPS