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

December 29, 2020 | education

| **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.

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