Answer:
By Thales' Rule (aka "the angle in a semicircle is a right angle"), since PR is a diameter,angle PQR is 90 degrees, i.e. PQ is perpendicular to QR, so their gradients multiply to -1.Thus 8/12 * -6/(a-9) = -1, so 12(a-9) = 48, so a-9 = 4, so a=13, as required.
Explanation: