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PC tangent wanted , starting with a semicircle

Source: Indian Postal Coaching 2008 set 4 p5

May 25, 2020
tangentgeometrysemicircleparallelcircle

Problem Statement

Let ω\omega be the semicircle on diameter ABAB. A line parallel to ABAB intersects ω\omega at CC and DD so that BB and CC lie on opposite sides of ADAD. The line through CC parallel to ADAD meets ω\omega again in EE. Lines BEBE and CDCD meet in FF and the line through FF parallel to ADAD meets ABAB in PP. Prove that PCPC is tangent to ω\omega.
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