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Suppose you have a given equilateral triangle $ABC$ and a semicircle is constructed on the side $BC$ with $BC$ as diameter, suppose also that points $K$ and $L$ divides the semicircle into three equal arcs, how do I prove that triangle $OLC$ is equilateral? Where $O$ is the centre of the circle.

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closed as off-topic by Sahiba Arora, Namaste, Daniel W. Farlow, Claude Leibovici, Trevor Gunn Jul 16 '17 at 4:20

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    $\begingroup$ Try showing $K$ and $L$ are on the midpoints of the sides of the equilateral $\endgroup$ – Shuri2060 Jul 16 '17 at 0:09
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    $\begingroup$ Specifically, try to show that $K\in AB$ and $L\in AC$ up to switching names. $\endgroup$ – user228113 Jul 16 '17 at 0:29
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Does this diagram shed some light?

enter image description here

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    $\begingroup$ You're always there to arrive with very informative graphics, nice +1 $\endgroup$ – Hushus46 Jul 16 '17 at 5:46

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