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equal segments in an isosceles inscribed trapezoid

Source: Nordic Mathematical Contest 2002 #1

September 24, 2017

isoscelestrapezoidgeometry

Problem Statement

The trapezium

{ABCD}

, where

{AB}

and

{CD}

are parallel and

{AD < CD}

, is inscribed in the circle

{c}

. Let

{DP}

be a chord of the circle, parallel to

{AC}

. Assume that the tangent to

{c}

at

{D}

meets the line

{AB}

at

{E}

and that

{PB}

and

{DC}

meet at

{Q}

. Show that

{EQ = AC}

.

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