# Question on coordinate geometry

Q. A circle $$C$$ of radius $$1$$ is inscribed in an equilaterateral traingle $$PQR$$. The points of contact of $$C$$ with sides $$PQ$$,$$QR$$,$$RP$$ are $$D$$, $$E$$ and $$F$$ respectively. The line $$PQ$$ is given by the equation $$y+\sqrt{3}x-6=0$$ and the point $$D$$ is $$(\frac{3\sqrt{3}}{2},\frac{3}{2}$$). Further it is given that the origin and the centre $$C$$ are on the same side of line $$PQ$$.

Find the coordinates of $$E$$, $$F$$,$$P$$,$$Q$$ and $$R$$.

Note by Krishna Jha
4 years, 6 months ago

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P: $$(\sqrt{3},3)$$, Q: $$(2\sqrt{3},0)$$, R: $$(0,0)$$

D: $$(\tfrac{3\sqrt{3}}{2},\tfrac32)$$, E: $$(\sqrt{3},0)$$, F: $$(\tfrac{\sqrt{3}}{2},\tfrac32)$$

The coordinates of $$P$$ and $$Q$$ (and of $$E$$ and $$F$$) can be swapped.

- 4 years, 6 months ago