Triangle PQR is equilateral with sides of length 10 cm. P, Q, and R are points on the circumference of a circle with centre O. Which one of the following is an expression, in centimetres, for the radius of the circle?

Answer:

12) D

Form right-angled triangles within the circle as shown below. The hypotenuse is QO. Note also, that QO is the radius of the circle.
M is the midpoint of QR. Since QR = 10 cm, QM = 5 cm.
Angle QMO is 90°. Angle QOM would be 60° as the 6 triangles split 360° into 6 equal angles near O.
sin60° QM/QO=5/QO
QO=5/sin60
So D is the answer.