Day 20: Chase for the Angle

Geometry Level 3

In triangle ABCABC, BA=BCBA=BC. The altitude ADAD is drawn, then a point PP is selected on it. Let EE be the foot of the perpendicular of ACAC from PP. EPEP intersects BCBC at QQ (both extended if necessary).

Given that ABC=40\angle ABC = 40^{\circ}, find the value of PQD\angle PQD.

This problem is part of the set Advent Calendar 2014.

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