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.