SOLUTION: A semi circle is inscribed inside a right triangle ABC with angle B = 90° such that its center O lies on side AC and divides it as AO = 15 cm and OC = 20 cm . find the radius of th

I changed your BO to OC because if it were BO then AC would not be divided by
the center O as is stated. However if it was really supposed to be BO, then tell 
me in the thank-you note form below and I'll redo it using BO = 20 instead of 
OC = 20.  




By similar triangles AEO and ODC:



Cross multiply. 

(Upper left times lower right equal upper right times lower left)





Square both sides.  Squaring a square root takes away the
square root and just leaves what's under it.  Squaring 
gives 



FOIL the left side:



Combine the middle terms on the left:



Subtract  from both sides:



Add -90000 to both sides:



Divide both sides by -625



Take positive square roots of both sides:



Edwin