Equation of the circle

Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3], and C[9, 4].

Correct answer:

e : e: (x-5)^2+(y-1)^2=12.5

Step-by-step explanation:

A=(1,2) B=(8,3) C=(9,4) S = (A+C)/2 x0=(Ax+Cx)/2=(1+9)/2=5 y0=(Ay+Cy)/2=((2)+4)/2=1  AB: a=1  a Ax+b Ay+c=0 a Bx+b By+c=0 1 1+b (2)+c=0 1 8+b (3)+c=0  2bc=1 3bc=8  Pivot:Row1Row2 3bc=8 2bc=1  Row232 Row1Row2 3bc=8 0.33c=4.33  c=0.333333334.33333333=13 b=38+c=38+13=7  b=7 c=13  AB: x+7y+13=0  v=a2+b2=12+72=5 27.0711  r=va x0+b y0+c=7.07111 5+7 1+133.5355  R=r2=3.53552=225=1221=12.5  e: (xx0)2+(yy0)2=r2 e:e:(x5)2+(y1)2=12.5=25:2

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Showing 1 comment:
I think the coordinate of D is (2,5) and ABCD is a square with side length of 5.sqrt(2) and the circle's radius is 5/sqrt(2). The equation of circle will be (x-5)2 + (y-1)2 = 25/2

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