If common tangents of x 2 + y 2 = r 2 and x 2 16 + y 2 9 = 1 forms a square, then the length of diagonal of the square is

Question

If common tangents of x 2 + y 2 = r 2 and x 2 16 + y 2 9 = 1 forms a square, then the length of diagonal of the square is,

MARKS App · Accepted Answer

Director circle of x 2 + y 2 = r 2 and x 2 16 + y 2 9 = 1 is same ⇒ x 2 + y 2 = 2 r 2 & x 2 + y 2 = 16 + 9 represents same circle ⇒ 2 r 2 = 25 ⇒ r = 5 2 side of square = 2 r = 5 2 diagonal of square = 2 (side of square) = 2 5 2 = 1 0

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