Given, three collinear points $A(3,1), B(7,-1)$ and $C(5,0)$. The length of a tangent drawn from $A$ to any circle that passes through $B$ and $C$ is ....... units.

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Aicharya · Accepted Answer

Since, we know that $A C \cdot A B=A T^2$ ...(i) by using distance formula $A C=\sqrt{(5-3)^2+(0-1)^2}$ $=\sqrt{4+1}=\sqrt{5}$ $\begin{aligned} A B & =\sqrt{(7-3)^2+(-1-1)^2} \\ & =\sqrt{16+4}=\sqrt{20}=2 \sqrt{5}\end{aligned}$ $\therefore \quad A T^2=\sqrt{5} \cdot 2 \sqrt{5} \Rightarrow A T=\sqrt{10}$

Given, three collinear points $A(3,1), B(7,-1)$ and $C(5,0)$. The length of a tangent drawn from $A$ to any…

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