Circle a ranch brand

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.

Scroll down for a solution to this problem.


Solution by Matthew Arcus.

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.

🤞 Don’t miss these puzzles!

Subscribe to the weekly geometry puzzle e-mail.

Leave a Reply

Your email address will not be published. Required fields are marked *

Optionally add an image (JPEG only)