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 $R$ .

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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.

Mark Hennings - 7 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$