Components of a Circle

Question

Find the measure of the Radius of the Circle

Answer 1

By properties of chords 24·24 = (2r - 12)·12; 2r - 12 = 48; 2r = 60; r = 30 ft

Answer 2

Hi Elizabeth J

r = 30

Thanks for the diagram it is loaded with right angles which can be easily closed by radius AE to form a nice right triangle.

The radius, r, is ED

The radius ED bisects chord AB at ED - 12 into two equal vertical lengths of 24

Draw radius AE, this radius forms a Right Triangle with the given height of 24 formed at ED - 12 and ED -12 is the base of the Right Triangle.

AE = ED = r

For the Right Triangle

(r - 12)² + 24² = r²

r² -24r + 144 + 576 = r²

Combine like terms and move the variables to one side of the equation

720 = r² - r² + 24r

r² cancels out

720 = 24r

Divide both sides by 24 to solve for r

720/24 = r

30 = r

I hope this help and can serve as a check against several other methods that can be used to find r.