The length of a common internal tangent to two circles is 7 and a common external tangent is 11. If the product of the radii of the two circles is p, then the value of p2 is
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Solution
We know that, the length of common internal tangent 7=√d2−(r1+r2)2⇒(r1+r2)2=d2−49⋯(1)
We know that, the length of common external tangent 11=√d2−(r1−r2)2⇒(r1−r2)2=d2−121⋯(2)
From equation (1) and (2), we get 4r1r2=72⇒4p=72∴p2=9