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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

Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear sindhuja


6886-2351_7662_untitled.JPG

in triangle AOD

AO2 =AD2 +OD2

r12  = a2/4  + (b-r1)2

r12  = a2/4  +  b2 +r1-2br1 

r1=a2+4b2/8b

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Badiuddin

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