Question

Find the coordinate of the circumcentre of ABC if A2,3 B4,-1 C5,2 Also find the circumradius?​

Answer 1

Given : A2,3 B4,-1 C5,2  vertex of triangle

To find : coordinate of the circumcentre & circumradius

Solution:

Circumecenter is at Equal distance from each vertex of triangle

A(2,3 ) B(4,-1) C (5,2)

Let say circumcenter = (x , y)

√(x - 2)² + (y - 3)² = √(x - 4)² + (y +1)² = √(x - 5)² + (y - 2)²  = Circum radius

Squaring

=>  (x - 2)² + (y - 3)² =  (x - 4)² + (y +1)² =  (x - 5)² + (y - 2)²

(x - 2)² + (y - 3)² =  (x - 4)² + (y +1)²

=> x²  - 4x + 4 + y² -6y + 9  = x² -8x + 16 + y² + 2y + 1

=> 4x - 8y = 4

=> x - 2y = 1    Eq1

√(x - 4)² + (y +1)² = √(x - 5)² + (y - 2)²

=> x² -8x + 16 + y² + 2y + 1 =  x² -10x + 25 + y² - 4y + 4

=> 2x + 6y = 12

=> x + 3y = 6    Eq2

Eq2 - Eq1

=> 5y = 5

=> y = 1

=> x = 3

( 3 , 1)  is the  circumcentre

Circum radius = √(x - 2)² + (y - 3)²  

= √(3 - 2)² + (1 - 3)²  

= √5  

( 3 , 1)  is the  circumcentre   & √5   is Circum radius

Learn more:

The circumcentre of the triangle formed by (2,-5), (2, 7), (4,7)

https://brainly.in/question/19157673

The circumcentre of the triangle formed by (2,-5) ,(2,7),(4,7)

https://brainly.in/question/17583145