# Formula for finding the coordinates of the Gergonne point of a triangle

Given any triangle with sides $$a$$, $$b$$ and $$c$$, and coordinates of vertices $$(x_{1},y_{1})$$, $$(x_{2},y_{2})$$ and $$(x_{3},y_{3})$$. What are the coordinates of its Gergonne point?

Note by Swapnil Das
2 years, 2 months ago

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There is an expression in terms of s,a,b,c. First find $$T_{a}$$ by section formula. Then compute$$\frac{AG_{e}}{G_{e}T_{A}}$$ by menelaus. Use the section formula again to find the gergonne point. The formula comes out to be $$\frac {\displaystyle \sum_{cyc} (s-b)(s-c)A}{\displaystyle \sum_{cyc} (s-b)(s-c)}$$. Here A is the complex number for the point A (this formula can easily be converted into cartesian form)

- 2 years, 2 months ago

Aah, I need help. @Ishan Singh

- 2 years, 2 months ago

Its easy but bit tedious. What have you tried?

- 2 years, 2 months ago

Tried infinitely many methods, but led to zero conclusions :P

- 2 years, 2 months ago