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A circle is inscribed in a right triangle the lengths of whose legs are 30 and 40.  Find the length of the line segment whose endpoints are the vertex of the right angle and the point of tangency, on the hypotenuse, of the inscribed circle.

 Dec 14, 2019
 #1
avatar+106539 
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The length  of  the hypotenuse  =  50

 

The  inradius  can be caculated as   ( sum of leg lengths -  hypotenuse)  / 2  =  (30 + 40 - 50) / 2  = 10

 

And the  coordinates  of the  incenter =  (10, 10)

 

So......the length of the segment is 

 

sqrt  (10^2 + 10^2) + 10  =

 

10sqrt (2)  + 10  =

 

10  [1 + sqrt (2)  ]  units

 

 

cool cool cool

 Dec 14, 2019

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