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length of projection, isosceles, circle (V Soros Olympiad 1998-99 Round 1 10.4)

Source:

May 25, 2024
geometry

Problem Statement

A straight line tangent to a circle circumscribed about an isosceles triangle ABCABC (AB=ACAB = AC) at point BB intersects straight line ACAC at point PP, EE is the midpoint of ABAB (fig.). What is the projection of DEDE onto ABAB if PA=aPA = a? https://cdn.artofproblemsolving.com/attachments/e/3/59c67e8f5eb3d399656d86613bc699c8baf1c1.png