Edited by Richard Walker, Wednesday 15 April 2026 at 22:10
I saw this problem on Mind Your Decisions.
At left is an equilateral triangle. From an arbitrary point in its interior we draw line segments to its vertices, making angles , and as shown. If now we construct a second triangle (right) whose sides are equal in length to these three line segments, as indicated by the tick marks—What will the angles of the new triangle be?
I have never seen this before and have not viewed the solution. But I have worked out what the answer must be, just not proved it yet. And it's a truly beautiful result.
I wonder if it can be generalised to non-equalateral triangle? Or to a square?
A Stunning Equilateral Triangle Problem
I saw this problem on Mind Your Decisions.
At left is an equilateral triangle. From an arbitrary point in its interior we draw line segments to its vertices, making angles , and as shown. If now we construct a second triangle (right) whose sides are equal in length to these three line segments, as indicated by the tick marks—What will the angles of the new triangle be?
I have never seen this before and have not viewed the solution. But I have worked out what the answer must be, just not proved it yet. And it's a truly beautiful result.
I wonder if it can be generalised to non-equalateral triangle? Or to a square?