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The pink circle with center D is tangent to the blue, green and red semicircles with centers B, C and A respectively as shown above. If the blue and green semicircles have radii 2 and 1 respectively, find the radius of the pink circle.

 

 Jan 23, 2021
 #1
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Let  a, b  be the coordinates of  D

Let the radius of the small circle     = r

 

Let A  =  (0,0)

B  =   (-1,0)

C  =  (2,0)

 

The  distance^2   between  A and D  is

 

a^2  + b^2  = (3 - r)^2

 

The distance^2   between  B   and D  is

 

(a + 1)^2  + b^2   =  (2 + r)^2

 

The distance ^2  between  C  and D  is

 

(a - 2)^2  + b^2  =  (1 + r)^2

 

Solving this system(without details)   we  have that

 

D   =(a, b)   =  ( 9/7  ,12/7)        r  = 6/7

 

Here's a graph  :  

 

cool cool cool

 Jan 24, 2021

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