MathDB

20

Part of 2015 India PRMO

Problems(1)

PRMO 2015. p20.

Source:

4/9/2024
20.20. The circle ω\omega touches the circle Ω\Omega internally at point P.P. The centre OO of Ω\Omega is outside ω.\omega. Let XYXY be a diameter of Ω\Omega which is also tangent to ω.\omega. Assume PY>PX.PY>PX. Let PYPY intersect ω\omega at z.z. If YZ=2PZ,YZ=2PZ, what is the magnitude of ∠PYX\angle{PYX} in degrees ??
geometrycirclesanglesTangents