Question

If (1, 2) is the centroid of an equilateral triangle and (–2, –2) is one of the vertices, then the equation of the incircle is-

• A. x2 + y2 – 2x – 4y – 20 = 0
• B. 4x2 + 4y2 –­ 8x – 16y – 5 = 0
• C. x2 + y2 + 4x + 4y – 17 = 0
• D. x2 + y2 + 4x + 4y + 17 = 0

Answer 1

Answer: (B)

4x2 + 4y2 –­ 8x – 16y – 5 = 0

Answer 2

In an equilateral triangle all centres coincide.

R = AG = 5

In-radius = GD = $\frac { 5 } { 2 }$

The equation of the in-circle is (x – 1)2 + (y ­– 2)2 =$\left( \frac { 5 } { 2 } \right) ^ { 2 }$or 4x2 + 4y2 – 8x – 16y – 5 = 0.