Let C 1 and C 2 be two circles of radius r 1 and r 2 respectively r 1 r 2 touching both the axes. If the two circles are orthogonal, then r 1 r 2 is equal to

Question

Let C 1 and C 2 be two circles of radius r 1 and r 2 respectively r 1 > r 2 touching both the axes. If the two circles are orthogonal, then r 1 r 2 is equal to, 2, 2 + 3, 3 + 2, 3

MARKS App · Accepted Answer

Let the equation of a circle touching both the axes be x - r 2 + y - r 2 = r 2 x 2 + y 2 - 2 r x - 2 r y + r 2 = 0 If the two given circles are orthogonal, then 2 - r 1 - r 2 + 2 - r 1 - r 2 = r 1 2 + r 2 2 ⇒ r 1 2 - 4 r 1 r 2 + r 2 2 = 0 ⇒ r 1 r 2 = 2 + 3

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