# Find the radius of the circle if the chord on which the angle of 30 degrees inscribed in the circle rests is 43 cm.

August 29, 2021 | education

| From the point O, the center of the circle, we construct the radii OA and OB to the ends of the chord AB.

The inscribed angle ACB rests on the arc AB, then the degree measure of the arc is equal to two degree measures of the inscribed angle. Arc AB = 2 * 30 = 60.

The central angle AOB also rests on the arc AB, then the value of the central angle is equal to the degree measure of the arc.

Angle AOB = 60.

Triangle AOB is equilateral, OA = OB = R, and since one of the internal angles is 60, then triangle AOB is equilateral, then R = AB = 43 cm.

Answer: The radius of the circle is 43 cm.

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