SOLUTION: Two circles have a 24-cm common chord, their centers are 14 cm apart, and the radius of one of the circles is 13 cm. Make an accurate drawing, and find the radius for the second ci

Question 1157985: Two circles have a 24-cm common chord, their centers are 14 cm apart, and the radius of one of the circles is 13 cm. Make an accurate drawing, and find the radius for the second circle in your diagram.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The segment joining the centers of the circles bisects the common chord.

So in the circle with radius 13, the common chord, the segment joining the centers of the circles, and the radius to an endpoint of the common chord form a right triangle with hypotenuse 13 and one leg 12; that makes the distance from the center of that circle to the common chord 5.

Since the length of the segment joining the two circles is 14, the distance from the center of the other circle to the common chord is 14-5=9.

Then in that other circle we have a right triangle with legs 9 and 12, making the hypotenuse 15.

And that hypotenuse is the radius of the second circle.

ANSWER: 15cm

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