First slide

Analysis of two circles in circles

Question

The length of a common internal tangent to two circles is 7 and that of a common external tangent is 11 . Then the product of the radii of the two circles is

Easy

Solution

From the figure,
$d^{2} = 11^{2} + {(r_{1} - r_{2})}^{2} - - - - - (1)$
From the figure, $d^{2} = 7^{2} + {(r_{1} + r_{2})}^{2} - - - (2)$
From (1) and (2),
$4 r_{1} r_{2} = 72 or r_{1} r_{2} = 18$

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