The center angle is 21 degrees larger than a sharp inscribed corner that rests on the same

The center angle is 21 degrees larger than a sharp inscribed corner that rests on the same circular arc. Find the inscribed angle.

Let the value of the central angle AOB be equal to X0, and the value of the inscribed angle ACB equal to Y0.

Then, by hypothesis, X – Y = 21. (1).

Since the value of the inscribed angle is equal to half the value of the central angle, then:

2 * Y = X. (2).

Let us solve the system of two equations 1 and 2 by the substitution method.

2 * Y – Y = 21.

Y = ASB = 21.

X = AOB = Y + 21 = 21 + 21 = 42.

Answer: The inscribed angle is 21.