Problem of the Day #42

POTD January 16, 2024
Author: XTL

Let ABC be an isosceles right triangle with AB=BC=1. Construct squares ABFG and BCED outside the triangle. If CG and AE intersect at H, and the area of triangle AHC is \frac{a}{b}, where a and b are relatively prime, positive integers, find a+b.

Try to solve this problem with the least amount of bash. No coordinates, no trig.