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Grade 11Differential Calculus

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

sindhuja P

16 Years agoGrade 11

1 Answer

Badiuddin askIITians.ismu Expert

Approved Tutor Answer16 Years ago

Dear sindhuja

in triangle AOD

AO² =AD² +OD²

r₁² = a²/4 + (b-r1)²

r₁² = a²/4 + b² +r1²-2br1

r₁=a²+4b²/8b

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Badiuddin

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