The triangle ABC is inscribed in the circle. Angle B = 66 Angle C = 84. The radius of the circle is 15. Find side BC.

In the triangle ABC, we define the value of the angle BAC.

Angle BAC = (180 – ABC – ACB) = (180 – 66 – 84) = 30.

The inscribed angle BAC rests on the BC arc, then the degree measure of the BC arc is equal to two values of the inscribed angle. Arc BC = 2 * 30 = 60, then the central angle BOC = 60.

In the triangle BОС OS and ОВ the radii of a circle, then the triangle BОС is isosceles, and since the angle BОС = 60, then the triangle BОС is equilateral, ВС = ОB = ОB = R = 15 cm.

Answer: The length of the BC side is 15 cm.