Connect 4 (blue) points B, C, D, E on a circle to some of the (orange) midpoints of non-adjacent arcs. (For example, C connects to J, E connects to L.) Intersect CJ with EL to get F, and intersect DK with BL to get G. Show that FG || JK.
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Solution
F and G are incentres of triangles with side DC (shown for F), so lie on the circle through C,D with centre L (Trillium theorem). Then it’s just circle geometry to show black angles are equal.