In the attached picture there is an equilateral triangle within a circumscribed circle. MW is a radius of the circle.
I wish to prove that MT = TW, i.e., that the triangle's edge cuts the radius into equal parts.
I thought perhaps to draw lines AM and AW and to try and prove that I get two identical triangles, but failed to do so. Is it possible to prove this without trigonometry, using Euclidean geometry only ?
I need this because this is the basis for the second way to solve the Bertrand paradox in probability. While I'm OK in probability, I couldn't prove this crucial geometric aspect of the problem. Any help will be most appreciated here.