This is an interesting geometry problem involving isosceles triangles, an equilateral triangle and a compass construction.
At first glance, the diagram resembles Langley’s Adventitious Angles, but the solution takes a different and highly satisfying path. By identifying key isosceles triangles and introducing a circle construction, we uncover hidden relationships that lead to an unexpected equilateral triangle — and from there, everything falls neatly into place.
This is a perfect example of how classical geometric tools like a compass and straightedge can reveal structure that isn’t immediately obvious.
📥 Free worksheet available
Download the problem and try it yourself before watching the full solution (link in description).
