Let ABCD be a rectangle with AB=a and BC=b.Suppose r₁ is the radius of the circle passing through A and B and touching CD ; r₂ is the radius of the circle passing through B and C and touching AD then prove that

r₁=a²+4b²/8b and r₂=b³+4a²b/8ab

Question

Let ABCD be a rectangle with AB=a and BC=b.Suppose r₁ is the radius of the circle passing through A and B and touching CD ; r₂ is the radius of the circle passing through B and C and touching AD then prove that

r₁=a²+4b²/8b and r₂=b³+4a²b/8ab

Badiuddin askIITians.ismu Expert · Answer

Dear sindhuja in triangle AOD AO 2 =AD 2 +OD 2 r 1 2 = a 2 /4 + (b-r1) 2 r 1 2 = a 2 /4 + b 2 +r1 2 -2br1 r 1 =a 2 +4b 2 /8b Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Askiitians Experts Badiuddin

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Let ABCD be a rectangle with AB=a and BC=b.Suppose r 1 is the radius of the circle passing through A and B and touching CD ; r 2 is the radius of the circle passing through B and C and touching AD then prove that r 1 =a 2 +4b 2 /8b and r 2 =b 3 +4a 2 b/8ab

Let ABCD be a rectangle with AB=a and BC=b.Suppose r₁ is the radius of the circle passing through A and B and touching CD ; r₂ is the radius of the circle passing through B and C and touching AD then prove that

r₁=a²+4b²/8b and r₂=b³+4a²b/8ab

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Let ABCD be a rectangle with AB=a and BC=b.Suppose r 1 is the radius of the circle passing through A and B and touching CD ; r 2 is the radius of the circle passing through B and C and touching AD then prove that r 1 =a 2 +4b 2 /8b and r 2 =b 3 +4a 2 b/8ab

Let ABCD be a rectangle with AB=a and BC=b.Suppose r1 is the radius of the circle passing through A and B and touching CD ; r2 is the radius of the circle passing through B and C and touching AD then prove that r1=a2+4b2/8b and r2=b3+4a2b/8ab

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Let ABCD be a rectangle with AB=a and BC=b.Suppose r₁ is the radius of the circle passing through A and B and touching CD ; r₂ is the radius of the circle passing through B and C and touching AD then prove that

r₁=a²+4b²/8b and r₂=b³+4a²b/8ab