Given 3 points A, B, C, define G so CG=CB and angle GCB is 120 degrees. Define M as the midpoint of side CH of the parallelogram CGAH. The green equilateral has side CM and the purple equilateral has side MB. Is AJK also equilateral?

Solution

Yes it is.

A simpler way: HA is a 120° rotation of CB, so comparing the yellow and black dashed segments, KA must be a 120° rotation of JK.

Given 3 points A, B, C, define G so CG=CB and angle GCB is 120 degrees. Define M as the midpoint of side CH of the parallelogram CGAH. The green equilateral has side CM and the purple equilateral has side MB. Is AJK also equilateral? https://t.co/FZ3l2H9fZz By @MarshallWBuck pic.twitter.com/hzI0aFYg3M

— Mirangu (@Mirangu1) May 24, 2024