1600
Shared Chord Power
Editorial
geometrycirclespower of a point
Two circles share a common chord ABAB. A point PP lies outside both circles on the line through AA and BB, with PA=5PA = 5 and PB=20PB = 20. A tangent segment PTPT is drawn from PP to the larger circle, touching it at TT. A line from PP through the interior of the smaller circle meets it at points XX and YY, with PX=4PX = 4. Find PYPY.

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