SOLUTION: A semicircle is inscribed inside a triangle ABC and with its center O lying on the side AC and Angle B = 90� and O divides AC such that AO = 15 cm and CO = 20 cm. Find the radius o

Question 894880: A semicircle is inscribed inside a triangle ABC and with its center O lying on the side AC and Angle B = 90� and O divides AC such that AO = 15 cm and CO = 20 cm. Find the radius of the circle.
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
A semicircle is inscribed inside a triangle ABC and with its center O
lying on the side AC and Angle B = 90� and O divides AC such that AO = 15 cm and CO = 20 cm. Find the radius of the circle.

  


Angles AOE and OCE are equal in measure.  Both are marked .

From the upper triangle,




From the lower triangle,




So setting the two expressions for r equal:



Divide both sides by 









Since tangent =  we draw a right
triangle with opposite=3 and adjacent=4.

hypotenuse = 




And since 
          
          

Edwin

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