<p>Circle O, center point is O, A,B,C,D 4 points along the circle. Connect AD, AB, BC, DC. AD and BC intersect at point E. Line OE divides angle AEC evenly. </p>

<p>Question: To proof AB = CD.</p>

<p>Circle O, center point is O, A,B,C,D 4 points along the circle. Connect AD, AB, BC, DC. AD and BC intersect at point E. Line OE divides angle AEC evenly. </p>

<p>Question: To proof AB = CD.</p>

<p>Can't give any magic formulas as it has been too long since I had to do that but Key is fact that line OE intersects angle AEC "evenly." A radius line like OE can only do that in a circle if AE = CE. From there everything flows. BE must = DE and AD must = BC; angle AEC must = angle BED which means angle AEB must equal CED. Thus the triangle formed by AEB has to be identical to CED (AE, the side of one triangle equals CE of the other, same for BE=DE, leaving the third side of the triangles AB and CD at the same length).</p>