The diameter AB and the chord AC are drawn in the circle. Find the angle BAC if the degree measures

The diameter AB and the chord AC are drawn in the circle. Find the angle BAC if the degree measures of the arcs AC and CB are 7: 2.

Since, by condition, AB is the diameter of the circle, the degree measure of the ACB arc will be equal to 180.

Let the degree measure of the arc BC is equal to 2 * X0, then, by hypothesis, the degree measure of the arc AC is equal to 7 * X0.

Then (2 * X + 7 * X) = 180.

9 * X = 18.

X = 180/9 = 200.

Then the degree measure of the arc BC = 2 * 20 = 40.

The inscribed angle BAC rests on the arc СB, then the value of the angle BAC = 40/2 = 20.

Answer: The value of the angle BAC is 20.