The arcs AGC and BHC have centers A and B respectively. Let s be the length of s

Question

The arcs AGC and BHC have centers A and B respectively. Let s be the length of segment AB and let r be the radius of the circle with center E. Each of the semicircle have diameter s/2. Express r in terms of s.

J6. The ares ÁGC and BEHC have centers A and B respectively. Let s be the leagth of egment AB sod ,6. The arcs AGC and BEC have centers A and B respectively. Let s be the length of segment AE and let r be the radius of the circle with center E. Each of the semicircles have diameter s/2. Express r in terms of s.

Explanation / Answer

in the given fig join DE and join FE join E to the place where two semicircles meet let this be X

then we have a rt angled triangle EXD

EX2+DX2 =DE2

EX = (r+s/2)

DX=s/2

DE=s

solving we get r= s/3

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