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A circle lies inside a quarter-circle, as shown below. The circle is tangent to side AO  and arc AB. Find the radius of the circle.

 Jun 23, 2024
 #1
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Let the center of the small circle = M

Draw MN  perpendicular to OA

We have right triangle ONM

 

MN^2 + ON^2 = OM^2

 

 

r^2 + 3^2  = (4 - r)^2

 

r^2 + 9 = r^2 - 8r + 16

 

8r =  7

 

r = 7/8

 

cool cool cool

 Jun 23, 2024

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