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.
+128473 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 : 
