A chord is drawn inside a circle, such that the length of the chord is equal to the radius of the circle. Now, two circles are drawn, one on each side of the chord, each touching the chord at its…
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A chord is drawn inside a circle, such that the length of the chord is equal to the radius of the circle. Now, two circles are drawn, one on each side of the chord, each touching the chord at its midpoint and the original circle. Let k be the ratio of the areas of the bigger inscribed circle and the smaller inscribed circle, then k equals
Answer and explanation
Correct answer: D - \(97 + 56\sqrt{3}\)
Chord = r so its distance from centre is r*sqrt(3)/2. Each inscribed circle has diameter equal to the segment height: r(1 - sqrt3/2) and r(1 + sqrt3/2). Radius ratio = (2+sqrt3)/(2-sqrt3) = 7+4sqrt3; area ratio = (7+4sqrt3)^2 = 97+56sqrt3.
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IPMAT Indore
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