Solution of the Week #556 - Triangle and Semicircle

If we call the radius ‘r’ and the height from the centre of the circle to the diagonal line ‘a’, then by Pythagoras we have:

49^2 = r^2 + a^2

Using intersecting chords theorem, 49*31 = (r+a)(r-a)

49*31 = r^2 – a^2

 If we take the first equation and subtract the second we get:

 49(49-31) = 2a^2

a^2 = 49*9

a = 21

 The height of the triangle is twice this distance ‘a’, and is therefore 42.