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].

Final 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  Row2−32​⋅ Row1→Row2 −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

Try another example


Help us improve the example. If you find a mistake, let us know. Thank you!



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





Tips for related online calculators
The line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
Do you have a linear equation or system of equations and are looking for a solution? Or do you have a quadratic equation?
See also our right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:

geometryalgebraarithmeticplanimetricsGrade of the word problem

 
We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Related math problems and questions: