A chord AB is drawn in a circle of radius 10. Find its length if the inscribed angle ACB is 50 degrees.

Let’s draw the radii ОА and ОВ to the edges of the chord AB.

The inscribed angle ACB rests on the arc AB, the degree measure of which is equal to two inscribed angles 2 * 50 = 100.

Then the central angle AOB, resting on the arc AB, is also equal to 100.

In triangle AOB, we apply the cosine theorem to determine the length of the chord AB.

AB ^ 2 = ОА ^ 2 + ОВ ^ 2 – 2 * ОА * ОВ * Cos100 = 10 ^ 2 + 10 ^ 2 + 2 * 10 * 10 * Сos100 = 100 + 100 – 200 * Cos100 = 100 * (2 + 2 * Cos100).

AB = 10 * √ (2 – 2 * Cos100) ≈ 15.32 cm.

Answer: The chord length is 15.32 cm