Find the radius of the other circle

Geometry Level 1

Two circles intersect and have a common chord 10 feet long. The radius of one circle is 13 feet long and the centers of the circles are 16 feet apart. Find the radius of the other circle.

40 \sqrt{40} 39 \sqrt{39} 43 \sqrt{43} 42 \sqrt{42} 41 \sqrt{41}

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1 solution

By Pythagorean Theorem

16 − x = 1 3 2 − 5 2 16 - x = \sqrt{13^2 - 5^2}

x = 4 x = 4 f e e t feet

Considering the other circle,

R = 4 2 + 5 2 = 41 R = \sqrt{4^2 + 5^2} = \sqrt{41} f e e t feet

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