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CE = EF wanted, tangents and secant from the same point

Source: China Northern MO 2010 p2 CNMO

October 28, 2022
geometryequal segments

Problem Statement

From a point PP exterior of circle āŠ™O\odot O, we draw tangents PAPA, PBPB and the secant PCDPCD . The line passing through point CC parallel to PAPA intersects chords ABAB, ADAD at points EE, FF respectively. Prove that CE=EFCE = EF. https://cdn.artofproblemsolving.com/attachments/8/c/bf15595bc341b917df30b3aa93067887317c65.png
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