Question 1157985
<br>
The segment joining the centers of the circles bisects the common chord.<br>
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.<br>
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.<br>
Then in that other circle we have a right triangle with legs 9 and 12, making the hypotenuse 15.<br>
And that hypotenuse is the radius of the second circle.<br>
ANSWER: 15cm<br>