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Let the circumcentre of Δ A B C is S - 1,0 and the midpoints of sides A B and A C are E ( 1 , - 2 ) and F - 2 , - 1 respectively, then the equation of the circumcircle of Δ A B C is

Options

  1. Ax + 1 2 + y 2 = 5
  2. Bx + 1 2 + y 2 = 10
  3. Cx + 1 2 + y 2 = 15
  4. Dx + 1 2 + y 2 = 1

Correct answer

B. x + 1 2 + y 2 = 10

Step-by-step solution

Slope of S F is 1 ⇒ Slope of A B is - 1 Now, the slope of E S is - 1 ⇒ Slope of A C is 1 Equation of A B is x + y + 3 = 0 Equation of A C is x - y - 3 = 0 So, point A is 0,3 S A = - 1 - 0 2 + 0 + 3 2 = 10 Hence, the equation of circumcircle is x + 1 2 + y 2 = 10

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