C 1 = (– 3, 0), r 1 = 3 , C 2 = (1, 0), r 2 = 1

C 1 C 2 = r 1 + r 2 So both circles touches each other externally at the origin. Common tangent at the origin is y-axis

y = mx + c be a direct common tangent to two circles = ± 3 and = ± 1

– 6m c + c 2 = 9 ⇒ 2 cm + c 2 = 1

cm = – 1 and c 2 = 3 ⇒ c = ± and m = ± 1/

Equation of common tangent are

y = x + , y = x – , x = 0

Both the lines makes an angle of 60 0 with x = 0 So the triangle formed by these lines is equilateral so that centroid, circumcentre, orthocentre are coincide with its incentre (1, 0), centre of smaller circle inscribed in the triangle PQR.