Question 1182839


Let, radius of the circle be{{{r}}} cm.

Suppose, the {{{10}}} cm long chord is {{{x}}} cm away from the center.

Thus, the {{{24}}} cm long chord should be {{{(17 - x)}}} cm away from the center.


We know, perpendicular drawn from center on any chord bisects the latter.


Thus,

{{{ r^2 = x^2 + (10/2)^2 = x^2 + 5^2}}}

{{{ r^2 = (17 - x)^2 + (24/2)^2 = (17 - x)^2 + 12^2}}}


Thus,

{{{ x^2 + 5^2 = (17 - x)^2 + 12^2}}}

{{{ x^2 - (17 - x)^2 = 12^2 - 5^2}}}

{{{17 * (2x - 17) = 17 * 7}}}

{{{ (2x - 17) = 7}}}

{{{2x = 24}}}

{{{x = 12}}}


So, 

{{{r^2 = 12^2 + 5^2 = 144 + 25 = 169}}}

{{{ r = 13}}}

The answer is: the radius of the circle is {{{13}}} cm