I think we can do it by diving equilateral triangle in 3 parts each with angle of 120.

length to the tangent from center will be the radius as 2 makes angle of 90 with tangent which is 1 side of triangle.

we need to find side opposite to angle of 60

Using 30:60:90 i.e root 1:root 3:2 ratio rule

Mapping it to gives 2y

x = 2 root 3

side of triangle = 2 * 2 root 3 = 4 root 3

area of triangle = side^2 * root 3/4

= 16 *3 * (root 3) /4
=12 root 3


Please tell if there is any direct formula.

nikhilgmat31 wrote:How to find the area of triangle if it outside a circle of Radius 2 ?

Hi Nikhil,

This question itself is incomplete as there can be infinite different scenarios of triangles outside the Circle of radius 2 so the area of the triangle will not be a consistent value.

Either you need to define whether it's the Equilateral Triangle or The triangle has to be bounded by some other constraint.

In case it's an equilateral Triangle then

(1/3) the Height of Equilateral Triangle = Radius of the Circle

i.e. (1/3){(Sqrt3)/2}Side of Equilateral Triangle = 2
i.e. Side of Equilateral Triangle = 4(Sqrt3)

i.e. Area of Triangle = (Root3 / 4)Side^2 = 12 Root3

In response to your item about any direct formula... you do not need one. As pointed out, we must know that this is an equilateral triangle to be able to do the math. The GMAT is testing your ability to relate concepts and draw conclusions from different sets of information, not memorize formulas.

I don't have a real question on this topic. But It was just to keep a formula handy for such equilateral triangle if all the 3 sides are tangent to circle.