Question

A triangle is inscribed in a circle. One side of the triagle has lenghth 12 cm, and the angle opposite that side measures 30 degrees. What is the diameter of the circle?

Answer 1

if a central angle and an inscribed angle subtend the same arc, the central angle is twice the inscribed angle.

So, the central angle is 60 degrees, and the chord length is equal to the radius.

SO, the diameter is 24.