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  • If the vertices of a triangle are and <img alt="\mathrm{\left(\frac{a}{2}, \frac{\sqrt{

If the vertices of a triangle are (0,0),(a, 0) and \mathrm{\left(\frac{a}{2}, \frac{\sqrt{3} a}{2}\right)},the coordinates of the incentre of the triangle are

Option: 1

\left(\frac{a}{3}, \frac{a}{2 \sqrt{3}}\right)


Option: 2

\left(\frac{a}{2}, \frac{a \sqrt{3}}{6}\right)


Option: 3

\left(\frac{a}{6}, \frac{a \sqrt{3}}{2}\right)


Option: 4

\left(\frac{3 a}{4}, \frac{\sqrt{3} a}{4}\right)


Answers (1)

best_answer

The given triangle is equilateral with each side equal to a and hence its incentre is same as the centroid of the triangle which is

\left(\frac{1}{3}\left(a+\frac{a}{2}\right), \frac{1}{3}\left(\frac{\sqrt{3} a}{2}\right)\right) \text { or }\left(\frac{a}{2}, \frac{\sqrt{3} a}{6}\right).

Posted by

Ritika Jonwal

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