Please combine these steps with the photograph provided below.
We know the longest side of the new right-angled triangle is 10, as it is simply the radius
We know one of the shorter sides would be 6 as line x cuts the chord, of length 12, in half
Therefore use Pythagoras Theorem to find X
So 10²= 6² + x²
X²= 10²-6²
X²=100-36= 64
X²=64
X= √64 = 8
X=8