Question

The center of the circle below is at P. If the central angle < APB measures 88 °, and the length of arc AB = 10 cm., find the radius. (round to the nearest tenth)

Answer 1

If the measure of the arc of the circle is 10 cm. Then the measure of the length of the radius will be 6.51 cm.

What is the relationship between central angle and angle on circumference?

Consider an arc of a circle.

Suppose it subtends θ angle on the rest of the part of the circumference (at any point). Then it subtends a 2θ angle on the center of that circle.

we know the formula

Are = θ/360 x 2πr

The center of the circle below is at P. If the central angle ∠APB measures 88° and the length of arc AB = 10 cm.

Then we have

    10 = 88 / 360 x 2πr

40.91 = 2πr

       r = 6.51 cm

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