I took a simple non-mathematical approach to this problem.

If i draw a circle that is completely inscribed inside a triagle with the sides as tangents to the circle, i have three points of contact

If i draw a cricle circumscribed about a triangle , the vertices of my triangle will lie on the circle hence i have again three points of contact

if i draw a circle such that the centre of the circle coincides with the center of the triange and the radius of my circle is less than the distance between the center of the circle and the vertice, then i will have two points of contact with each side of the triangle. In this case i will have 2 points on each side of the triangle. Hence i will have 6 POINTS OF CONTACT

LAST ANSWER CHOICE HAS 6 POINTS OF CONTACT HENCE IT IS THE CORRECT CHOICE.

HARDCORE MATH APPROACH:

Equation of circle = x^2 + y^2 = r^2 ------------- Quadratic Equation
Equation for side of triangle = mx +y = c--------------- linear Equation

If you solve for each side you have will have two points for each side and the circle. Giving you a total of 6 solutions.

Hope this helps

HARDCORE MATH APPROACH:

Equation of circle = x^2 + y^2 = r^2 ------------- Quadratic Equation
Equation for side of triangle = mx +y = c--------------- linear Equation

If you solve for each side you have will have two points for each side and the circle. Giving you a total of 6 solutions.

Hope this helps

I think for this question it is easier to just draw it out.





Best,
Rajiv
Founder of www.gmathints.com

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