Question

Triangle XYZ is inscribed in a circle, where XY is a diameter of the circle, XZ=16 units, and YZ=30 units. What is the diameter, in units, of the circle? A. 38 units. B. 34 units. C. 25 units. D. 32 units.

Answer 1

Because XY is a diameter, angle XZY is a right angle (Thales' theorem). So XZ and YZ are the legs of a right triangle and XY is the hypotenuse:

XY = sqrt(16^2 + 30^2) = sqrt(256 + 900) = sqrt(1156) = 34.

Answer: B.