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A semicircle with radius a is inscribed in a rectangle with its diameter along one...........Solve for the value of a/b.

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A semicircle with radius a is inscribed in a rectangle with its diameter along one side of the rectangle. A circle with radius b is then inscribed so it is tangent to the rectangle and the semicircle, as shown.
Solve for the value of a/b.

enter image description here

posted Jun 11 by Aman

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1 Answer

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(√2+1)/(√2-1) or 5.83


See attached
enter image description here

As we can see above
AD=AB+BC+CD
AB= b√2, BC=b, CD=a, AD=a√2
a√2=a+b+b√2
a√2-a=b+b√2
a(√2-1)=b(√2+1)
a/b=(√2+1)/(√2-1)= 5.83

answer Jun 12 by Hanifa Mammadov



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