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How do you find the Circumradius of a triangle with given vertices?

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How do you find the Circumradius of a triangle with given vertices?

Once we have a circumcenter we will find circumradius by calculating the distance of this point and any vertex of the triangle. Let us say A = (1, 1), B = (2, -1) and C = (3, 2). Now let O = (x, y) be the circumcenter of the triangle.

How do you find the circumcenter of a triangle with coordinates?

Steps to find the circumcenter of a triangle are:

  1. Calculate the midpoint of given coordinates, i.e. midpoints of AB, AC, and BC.
  2. Calculate the slope of the particular line.
  3. By using the midpoint and the slope, find out the equation of the line (y-y1) = m (x-x1)
  4. Find out the equation of the other line in a similar manner.
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How do you find the Circumcircle of a triangle?

Equation of the circumcircle of the triangle formed by the co-ordinate axes and the line 3X + 4y =24 is:

  1. A. x2+y2−8x−6y=0.
  2. B. x2+y2+8x−6y=0.
  3. C. x2−y2+8x−6y=0.
  4. D. x2+y2−8x+6y=0.

How do you find circumradius?

The circumradius of a polygon is the radius of its circumcircle. The formula for the circumradius of a triangle with sides of lengths a, b, and c is (abc) / sqrt((a + b + c)(b + c – a)(c + a – b)(a + b – c)), and for a regular polygon with n sides of length s, it is s / (2sin(π / n)).

How do you find the coordinates of circumradius?

  1. To Find :- The circum – radius. Let, A ( 8,6 ) , B ( 8,-2 ) and C ( 2,-2 ) be the vertices of the given triangle. And also let P ( x,y ) be the circumcenter of this triangle. PA = PB = PC.
  2. y = 2. And. PB² = PC²
  3. x = 5. So, the coordinates of the circumcentre P are ( 5,2 ) Also Circum-radius = PA = PB = PC = √(5-8)² + (2-6)²

What is meant by circumcircle of a triangle?

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Definition of circumcircle : a circle which passes through all the vertices of a polygon (such as a triangle)

What is the area of circumcircle?

The area and perimeter of a circumcircle are the same as they would be for any other circle. If a circle has radius r, then the formulas for the area and perimeter of that circle, are as follows: Area of a circle = πr2. Perimeter of a circle = 2πr.