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Tangents drawn from point of intersectio...

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

A

equilateral triangle

B

right angle triangle

C

obtuse angle triangle

D

isosceles triangle and `/_ABC = (pi)/(6)`

Text Solution

Verified by Experts

The correct Answer is:
A

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.
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