The incentre of the triangle with vertices ( 1 , 3 ) , ( 0 , 0 ) and ( 2 , 0 ) is [2000]

Question

The incentre of the triangle with vertices $(1, \sqrt{3}), (0, 0)$ and $(2, 0)$ is [2000]

Smart Achievers · Accepted Answer

(4)

Let $(1, \sqrt{3}), (0, 0)$ and $(2, 0)$ are the coordinates of vertices A, O, B of $∆ A B C$ .

$∴$ AO = OB = AB. So, it is an equilateral triangle and the incentre coincides with centroid.

$∴$ Incentre $= (\frac{0 + 1 + 2}{3}, \frac{0 + 0 + \sqrt{3}}{3}) = (1, \frac{1}{\sqrt{3}})$

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