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

 Mar 17, 2024
 #1
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Let the center of  the small circle =  C

Let the tangent point of  the circle with OA = D

 

Triangle  OCD  is  right such that

 

OD^2  + DC^2  = OC^2

 

3^2  + r^2  = (5 - r)^2

 

9 + r^2  = r^2  - 10r  + 25

 

10r  = 16

 

r =  16 / 10   =  1.6

 

cool cool cool

 Mar 18, 2024

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