The diagonals of a rhombus are 14 and 48. Find the radius of the circle inscribed in the rhombus.
+128407 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
