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?

Guest Feb 14, 2020

#1**+2 **

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

CPhill Feb 14, 2020

#2**+1 **

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 **

Dragan Feb 16, 2020