Problem

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Tags: geometry



Let ω be a semicircle with AB as the bounding diameter and let CD be a variable chord of the semicircle of constant length such that C,D lie in the interior of the arc AB. Let E be a point on the diameter AB such that CE and DE are equally inclined to the line AB. Prove that (a) the measure of CED is a constant; (b) the circumcircle of triangle CED passes through a fixed point.