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  • The number of tangents that can be drawn from the point <img alt="\mathrm{\left(\frac{5}{2}, 1\right)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cleft%28%5Cfrac%7B5%7D%7B2

The number of tangents that can be drawn from the point \mathrm{\left(\frac{5}{2}, 1\right)} to the circle passing through the points \mathrm{(1, \sqrt{3}),(1,-\sqrt{3})\, \, and\, \, (3,-\sqrt{3})} is

Option: 1

1


Option: 2

0


Option: 3

2


Option: 4

None of these


Answers (1)

best_answer

The triangle is right angled.
The circumcircle is \mathrm{(x-2)^2+(y-0)^2=2^2\, \, or \, \, x^2+y^2-4 x=0}

\mathrm{ \begin{aligned} & \left(x_1, y_1\right)=\left(\frac{5}{2}, 1\right) \\ \Rightarrow & S_{11}=\frac{25}{4}+1-10<0 \\ \therefore & \left(\frac{5}{2}, 1\right) \text { lies inside the circle. } \end{aligned} }

There is no tangent from it.

Posted by

Ritika Jonwal

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