2025 HMMT November General Round Problem 5

Let A, B, C, and D be points on a line in that order. There exists a point E such that \angle AED = 120^\circ and triangle BEC is equilateral. Given that BC = 10 and AD = 39, compute |AB - CD|.

Answers are checked by value, so any equivalent form is accepted: 1/2, \frac{1}{2} and 0.5 all count as the same answer.

Full credit goes to HMMT for authoring these problems. This problem is from the November 2025 contest; the official solution is available on the HMMT archive. HMMT is not affiliated with or endorsing TopsOJ in any way.