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

 

 

AB = 10.

 Jan 14, 2024

Best Answer 

 #1
avatar+36919 
+1

From the diagram below, using Pythagorean theorem:

2.5^2 + (5-r)^2  = (2.5+r)^2 

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

-15r = -25 

r = 1  2/3  units             ( and diameter = 2 * r = 3 1/3   units )  

 

 Jan 14, 2024
edited by ElectricPavlov  Jan 14, 2024
 #1
avatar+36919 
+1
Best Answer

From the diagram below, using Pythagorean theorem:

2.5^2 + (5-r)^2  = (2.5+r)^2 

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

-15r = -25 

r = 1  2/3  units             ( and diameter = 2 * r = 3 1/3   units )  

 

ElectricPavlov Jan 14, 2024
edited by ElectricPavlov  Jan 14, 2024

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