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Semicircles are constructed on AB, AC, and BC. Find the radius of the circle.

 

 

AB = 10.

 Mar 8, 2024
 #1
avatar+128794 
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Let O be the midpoint of  MB......this is also the  center of the the semi-circle on the right

MO = AB / 4 =  10/4 =  2.5

MC = 5 - r      where  5 is the radius of the large semi-circle and r is the radius of the circle

CO = 2.5 + r

 

We have a right triangle such that

 

MC^2 + MO^2 = CO^2

 

(5 - r)^2   + 2.5^2 = (2.5 + r)^2

 

r^2 -10r + 25 +  6.25  + r^2 + 5r + 6.25

 

-10r + 25  = 5r

 

15r  = 25

 

r = 25/15  =  5/3  

 

cool cool cool

 Mar 8, 2024

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