If $A(2+3 \cos \alpha,-3+3 \sin \alpha), B\left(2+3 \cos \left(\alpha+\frac{2 \pi}{3}\right),-3+3 \sin \left(\alpha+\frac{2 \pi}{3}\right)\right)$
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If $A(2+3 \cos \alpha,-3+3 \sin \alpha), B\left(2+3 \cos \left(\alpha+\frac{2 \pi}{3}\right),-3+3 \sin \left(\alpha+\frac{2 \pi}{3}\right)\right)$ and $C\left(2+3 \cos \left(\alpha+\frac{4 \pi}{3}\right),-3+3 \sin \left(\alpha+\frac{4 \pi}{3}\right)\right)$ be the angular points of a $\triangle ABC$ then incentre of that triangle is

(1) $(3,2)$

(2) $(0,0)$

(3) $(2,-3)$

(4) $(-2,-3)$

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ANSWER : The option of this question will be (3).

EXPLANATION / HINT :

A, B, C lie on a circle of center (2, -3) and of radius 3 and they form equilateral triangle

∴ Incentre is (2, -3)

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