find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7,1),B(3,5) and C(2,0) are given
Answers
=(7+3+2/3, 1+5+0/3)
= (12/3,6/3)
=(4, 2)
Given : ∆ABC A(7,1),B(3,5) and C(2,0
To find : the coordinates of circumcentre and radius of circumcircle
Solution:
A(7,1), B(3,5) , C(2,0)
Circumcenter where perpendicular bisector meets
AB slope = (5 - 1)/(3 - 7) = 4/-4 = -1
Slope of perpendicular to AB = 1
Mid point of AB = (7+ 3)/2 , ( 1 + 5)/2 = 5 , 3
Equation of perpendicular bisector of AB
y = x + c
=> 3 = 5 + c
=> c = -2
y = x - 2
=> x - y = 2
AC slope = (0 - 1)/( 2- 7) = -1/-5 = 1/5
Slope perpendicular to AC = - 5
Mid point of AC = 9/2 , 1/2
y = -5x + c
=> 1/2 = -45/2 + c
=> c = 23
=> y = -5x + 23
=> 5x + y = 23
x - y = 2
5x + y = 23
=> 6x = 25
=> x = 25/6
y = 13/16
( 25/6 , 13/6 )
coordinates of circum centre ( 25/6 , 13/6 )
Radius = √(25/6 - 7)² + (13/6 - 1)² = √(25/6 - 3)² + (13/6 - 5)² = √(25/6 - 2)² + (13/6 - 0)²
Radius = 13√2/3
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