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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
3 years, 11 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.

Mark Hennings - 3 years, 11 months ago

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