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  2b−c=1 3b−c=8  Pivot:Row1↔Row2 3b−c=8 2b−c=1  Row2−32​⋅ Row1→Row2 3b−c=8 −0.33c=−4.33  c=−0.33333333−4.33333333​=13 b=38+c​=38+13​=7  b=7 c=13  AB: x+7y+13=0  v=a2+b2​=12+72​=5 2​≐7.0711  r=va⋅ x0​+b⋅ y0​+c​=7.07111⋅ 5+7⋅ 1+13​≐3.5355  R=r2=3.53552=225​=1221​=12.5  e: (x−x0​)2+(y−y0​)2=r2 e:e:(x−5)2+(y−1)2=12.5=25:2

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Showing 1 comment:
Ema
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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