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Let $K$ be a circle with center $B$ and $A,C,D$ points on the circle. Further let $\overline{BE}$ be the perpendicular bisector of $\overline{AC}$.
Then it happens to be that the line $\overline{DE}$ is the angle bisector of $\sphericalangle CDA$, but how does one proof this?
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$\begingroup$Angles subtended by an arc at the center of a circle are double those at the circumference:
$$\angle ADE = {1\over 2}\angle ABE = {1\over 2}\angle EBC = \angle EDC$$
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