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If A(0,0),B(1,0) and $C (\frac{1}{2}, \frac{\sqrt{3}}{2})$ are vertices of a triangle, then the centre of the circle for which the lines AB,BC and CA re tangents is

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(12,14)

(32,32)

(12,123)

(12,−13)

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detailed solution

Correct option is C

AB=AC=BC=1So, triangle is an equilateral.Thus, incentre coincoide with centroid.Centre of the circle touching all the three sides of triangle is incentre.Therefore, incentre is (0+1+123,0+0+323)≡(12,123)

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If A(0,0),B(1,0) and C(12,32) are vertices of a triangle, then the centre of the circle for which the lines AB,BC and CA re tangents is

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If A(0,0),B(1,0) and $C (\frac{1}{2}, \frac{\sqrt{3}}{2})$ are vertices of a triangle, then the centre of the circle for which the lines AB,BC and CA re tangents is