Given a circle with center O, points ABC lie on the circle. angle BAC = 45 degrees, diameter 16 cm. Find chord BC.

Because the angle BAC-inscribed, then the arc of the BC, on which it rests, is equal to 2 * 45 = 90 degrees. The central angle of the ВOC rests on the same arc, therefore the angle ВOС = 90 degrees. The BOС triangle is isosceles, because BO = OC = d / 2 = 16/2 = 8 cm. BC is the hypotenuse of the triangle BOC, BO and OC are cathets, therefore √ BC = √8 ^ 2 + 8 ^ 2 = √64 + 64 = √128 = 8√ 2 cm.