A small circle inscribed between two indentic big circle. The three circles are also tangent to a line. If the radius of the big circle is 10, find the radius of the small circle
We can form a right triangle with legs of 10-r , 10 and a hypotenuse of 10+ r
So we have that
(10-r)^2 + 10^2 = (10 + r)^2 simplify
r^2 - 20r + 100 + 100 = r^2 + 20r + 100
-20r + 200 = 20r + 100
100 = 40r
r = 100 / 40 = 5/2 = 2.5
