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
Answers
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
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Answer:
Step-by-step explanation: