In a circle, the inscribed angle is 75 degrees; it rests on the arc ab; the area of the sector with the

In a circle, the inscribed angle is 75 degrees; it rests on the arc ab; the area of the sector with the arc ab is 5 / 3pi cm ^ 2. Find the radius of the circle.

Let’s draw the radii ОА and ОВ of the circle.
The value of the inscribed angle ACB = 750, then the degree measure of the arc on which the angle rests is 75 * 2 = 1500.
The central angle ABO is equal to the degree measure of the arc AB. Angle AOC = 1500.
Let’s apply the sector area formula.
Ssec = π * R ^ 2 * AOB / 360.
R ^ 2 = 360 * Ssec / π * AOB = 360 * (5/3) * π / π * 150 = 4.
R = 2 cm.
Answer: The radius of the circle is 2 cm.