the circumcenter of the triangle formed by (-2,3),(7,4)and(4,0)is
Answers
Given : triangle formed by (-2,3),(7,4)and(4,0)is
To find : circumcentre of the triangle
Solution:
Let say ( x , y ) is the circumcenter of triangle formed by
(-2,3),(7,4)and(4,0)
Distance of circumcenter from each vertex is same
(x + 2)² + (y -3)² = (x - 7)² + (y - 4)² = (x - 4)² + (y)²
(x + 2)² + (y -3)² = (x - 7)² + (y - 4)²
=> x² + 4x + 4 + y² -6y + 9 = x² - 14x + 49 + y² -8y + 16
=> 18x + 2y = 52
(x - 7)² + (y - 4)² = (x - 4)² + (y)²
=> x² - 14x + 49 + y² -8y + 16 = x² - 8x + 16 + y²
=> 6x + 8y = 49
18x + 2y = 52
6x + 8y = 49
=> 22y = 95
=> y = 95/22
or 66x = 159
=> x = 53/22
( 53/22 ,95/22) the circumcentre of the triangle formed by (2,-5), (2, 7), (4,7)
option 1 is correct
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