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# geometry

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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? Feb 14, 2020

#1
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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   Feb 14, 2020
#2
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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  Feb 16, 2020
edited by Dragan  Feb 16, 2020
edited by Dragan  Feb 17, 2020
#3
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I like your drawings Dragan Melody  Feb 16, 2020
#4
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Thanks, Melody! That's how we did 50+ years ago. Dragan  Feb 16, 2020
edited by Dragan  Feb 16, 2020
edited by Dragan  Feb 16, 2020
#5
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Yes, I know Still Geogebra is really fun to use. It is a free download.

Maybe you would like to try it sometime.. I like your neat hand-drawn pics though. Melody  Feb 16, 2020
#6
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Hey Dragan,

Why is your pic no longer displaying??? Melody  Feb 16, 2020
edited by Melody  Feb 16, 2020
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Thanks for GeoGebra! Dragan  Feb 18, 2020
edited by Dragan  Feb 18, 2020
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I found GeoGebra a little hard at first.

But persist because you will get the hang of it and it is a lot of fun to use.

Melody  Feb 18, 2020