Tangents drawn from point of intersection A of circles `x^2+y^2=4 and (x-sqrt3)^2+(y-3)^2= 4` cut the line joinihg their centres at B and C Then triangle BAC is

Options

A. equilateral triangle
B. right angle triangle
C. obtuse angle triangle
D. isosceles triangle and `/_ABC = (pi)/(6)`

Answer

A

Explanation

Radii of the circles are same
`rArr AB = AC`
Also, if `theta` is the angle between the tangents, then
`cos theta = (12-4-4)/(2(2)(2)) =(1)/(2)`
`rArr theta = (pi)/(3)`
Hence, `DeltaABC` is an equilateral triangle.