Question

Two circles touch each other internally. The difference of their areas is $119\pi {cm}^2$ and the distance between their centers is $7cm$. Find the radii of circles.

Answer 1

$r_1-r_2=7$cm

$\pi r_1^2-\pi r_2^2=119\pi c{m}^2$

$r_1^2-r_2^2=119$

$(r_1-r_2)(r_1+r_2)=119$

$r_1+r_2=\frac{119}{7}=17$

$r_1+r_2=17$

$r_1-r_2=7$

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$2r_1=24$

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$r_1=12$cm and $r_2=5$cm.