AB is a line segment of length 24 cm and C i | vedclass

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(C) Let the radius of the small semicircles be $R_1 = R_2 = 6 \ cm$ (since $AC = CB = 12 \ cm$,their radii are $6 \ cm$).Let the radius of the large s

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$4$

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(C) Let the radius of the small semicircles be $R_1 = R_2 = 6 \ cm$ (since $AC = CB = 12 \ cm$,their radii are $6 \ cm$).Let the radius of the large semicircle be $R = 12 \ cm$.Let the radius of the required circle be $r$ and its center be $D$.The distance from the center of the large semicircle (point $C$) to the center of the required circle $D$ is $R - r = 12 - r$.The distance from the center of the small semicircle (let's say $O_1$,which is the midpoint of $AC$) to the center $D$ is $R_1 + r = 6 + r$.In $\Delta DO_1C$,by the Pythagorean theorem:$CD^2 + O_1C^2 = DO_1^2$$(12 - r)^2 + 6^2 = (6 + r)^2$$144 - 24r + r^2 + 36 = 36 + 12r + r^2$$144 = 36r$$r = 4 \ cm$.

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