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प्रश्न
A(-2, -3), B(-1, 0) and C(7, -6) are the vertices of a triangle. Find the circumcentre and the circumradius of the triangle.
उत्तर
Circumcircle of MBCwill pass through the vertices A,B and C. AB = OB (radii of same circle)
⇒ OA2 =OB2
(x+2)2 +(y+3)2=(x+1)2 +Y2
⇒ 4x + 4 + 9 + 6y = 2x + 1
⇒ 2x+6y=-12 .....(1)
OB =OC (radii of same circle)
⇒ OB2 =OC2
(x + 1)2 + y2 =(x - 7)2 +(Y+ 6)2
⇒ 2x + 1= 49 - 144 x + 36 + 12
⇒ 16x - 12=8y
⇒ 4x - 3y = 21 ....(2)
On solving (1) and (2)
4x + 12y = -24
4x - 3y = 21
- + -
_____________
15 y = - 45
y = - 3
from (1)
2x + 6(-3) = -12
⇒ 2x = 6
⇒ x = 3
Circumcentre of Δ ABC is (3, - 3)and
Circumradius = `sqrt ((3 + 2)^2 + (-3 + 3)^2) = sqrt 25 = 5 "units"`
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