Question

the circumcenter of the triangle with vertices of a is equals to 5, 12 b is equals to 12, 5 C is equals to2 root 13 ,3root 13

Answer 1

Given : triangle with vertices of A is equals to 5, 12

B  is equals to 12, 5

C is equals to 2√13 ,3√13

To Find : circumcenter of the triangle

Solution:

Let say O (x , y) is the circumcenter of triangle

circumcenter will be equidistant from all three vertex

OA = OB = OC

OA² = OB² = OC²

OA²  = (x - 5)² + (y - 12)²

OB²  = (x - 12)² + (y - 5)²

OC² = (x - 2√13)² + (y -3√13 )²

(x - 5)² + (y - 12)² =  (x - 12)² + (y - 5)²

=> x²  - 10x + 25 + y²  -24y + 144 = x²  - 24x + 144 + y² - 10y + 25

=> 14x  = 14y

=> x = y

OA²  = (x - 5)² + (x - 12)²

OC² = (x - 2√13)² + (x -3√13 )²

(x - 5)² + (x - 12)² =  (x - 2√13)² + (x -3√13 )²

=> x² - 10x  + 25 + x² - 24x  + 144  = x²  - x4√13  + 52 + x²  - x6√13  + 117

=>   -34x  = -10x√13

=> x( -34 + 10√13 ) = 0

=> x = 0

y= 0

(0 , 0)  is the circumcenter of the triangle

Learn More:

Find the co-ordinates of the circumcentre of the triangle formed by ...

brainly.in/question/12127230

find the coordinates of circumcentre and radius of circumcircle of ...

brainly.in/question/3772960

Answer 2

Answer:

Step-by-step explanation: