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The diagonals of a rhombus are 14 and 48.  Find the radius of the circle inscribed in the rhombus.

 Dec 16, 2019
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See  the following image :

 

 

The slope  of  the line containig  side  BD   =     [ 0 - 24 ] / [ -7 - 0]  = 24/7

And the equation of  line containg this segment is given by

y = (24/7)x  + 24        multiply this  by  7

7y  = 24x  +  168     put into  standard form

24x - 7y + 168  = 0       [ Ax  + By  + C  =  0  ]

 

The circle will be centered at  (0, 0)

And we can use  the formula for the  distance from  point (m, n) = (0,0) to  the line we found = the radius of the  circle

 

So

 

l  Am  + Bn  + C l             l  24(0) - 7(0)  + 168  l             168

_______________ =     ___________________   =     _____   =   6.72 =  AF

  √[ A^2 + B^2 ]                  √ [ 24^2 + 7^2 ]                       25

 

 

 

cool cool cool

 Dec 16, 2019
edited by CPhill  Dec 16, 2019
edited by CPhill  Dec 16, 2019

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