Find-the-equation-and-radius-of-the-circumcircle-of-the-triangle-formed-by-the-three-line-2y-9x-26-0-9y-2x-32-0-11y-7x-27-0-

Question Number 15868 by tawa tawa last updated on 14/Jun/17

Find the equation and radius of the circumcircle of the triangle formed by

the three line :

2 y - 9 x + 26 = 0

9 y + 2 x + 32 = 0

11 y - 7 x - 27 = 0

Answered by Tinkutara last updated on 14/Jun/17

2 y - 9 x + 26 = 0 \dots (i)

9 y + 2 x + 32 = 0 \dots (i i)

11 y - 7 x - 27 = 0 \dots (i i i)

Solving (i) and (i i), A = (2, - 4)

Solving (i i) and (i i i), C = (- 7, - 2)

Solving (i i i) and (i), B = (4, 5)

Slope of (i) = \frac{9}{2} and that of (i i) = \frac{- 2}{9}

so A B ⊥ A C and Δ A B C is right angled

at A . ∴ Circumcenter = midpoint of B C

and circumradius = \frac{B C}{2} .

Circumcenter = (- 1.5, 1.5) and

circumradius = \frac{\sqrt{170}}{2}

Equation of circumcircle =

{(x + 1.5)}^{2} + {(y - 1.5)}^{2} = \frac{170}{4} = 42.5

Commented by tawa tawa last updated on 14/Jun/17

God bless you sir .