Circles M & N (centered at points M and N respectively) are tangent to each other and to AC & BC. If the radius of the circle with center N is 5/(1+sqrt2) m, what is the radius of M, in meters?
+128408 Let the radius of M = m
We can from a right triangle
Two legs = (m - 5/ [ 1 + sqrt (2) ]
And the hypotenuse = m + 5 / [ 1 + sqrt (2) ]
So.....by the pythagorean Theorem we have that
(m - 5/ [ 1 + sqrt (2) ] )^2 + ( m - 5/ [1 + sqrt (2) ] )^2 = ( m + 5 / [1 + sqrt (2) ] )^2
Solving this for the larger value of m we get that m = 5 ( 1 + sqrt (2) ) ≈ 12.07 m
+1486 NO = 5/(1+sqrt(2)) = 2.071068294
MO = r / sin(45) = 2.92893287
MN = MO - NO =0.857864576
Proportion: MN : NO = MT : TR
Radius of circle "M" is: TR = 12.071068 m 
