Straight Line and Pair of Straight Lines 1 Question 29
29. The incentre of the triangle with vertices $(1, \sqrt{3}),(0,0)$ and $(2,0)$ is
(2000, 2M)
(a) $1, \frac{\sqrt{3}}{2}$
(b) $\frac{2}{3}, \frac{1}{\sqrt{3}}$
(c) $\frac{2}{3}, \frac{\sqrt{3}}{2}$
(d) $1, \frac{1}{\sqrt{3}}$
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Solution:
- Let the vertices of triangle be $A(1, \sqrt{3}), B(0,0)$ and $C(2,0)$. Here, $A B=B C=C A=2$.
Therefore, it is an equilateral triangle. So, the incentre coincides with centroid.
$$ \begin{array}{ll} \therefore & I \equiv \frac{0+1+2}{3}, \frac{0+0+\sqrt{3}}{3} \\ \Rightarrow & I \equiv(1,1 / \sqrt{3}) \end{array} $$
