An isosceles triangle is inscribed in a circle with a radius of 13. It is known that the sine of the angle

An isosceles triangle is inscribed in a circle with a radius of 13. It is known that the sine of the angle at the base of the triangle is 12/13. The OMOM radius intersects at right angles the lateral side at point K. Find the line length OK.

Find the angle M sine, which is 12/13. Use the Bradis table sin12 / 13 = sin 0.92 = 67 degrees.
Angle A = 180 – (angle M + angle B) = 180- (67 + 67) = 180-134 = 46 degrees. Since AC for an isosceles triangle is a bisector, then the angle OAK = 1 / 2angleA = 1/2 * 46 = 23 degrees. Outside by definition sin OAK = OK / OA, then OK = OA * sinOAK = 13 * 0.3 = 3.9.