The line $2x - y + 1 = 0$ is tangent to the circle at the point $(2,5)$ and the centre of the circle

Question

The line $2x - y + 1 = 0$ is tangent to the circle at the point $(2,5)$ and the centre of the circles lies on $x - 2y = 4$. The radius of the circle is:

Accepted Answer

Sol. [Key Concept: Tangent at a known point + centre on a given line $\Rightarrow$ solve for the centre/radius.]$$\begin{matrix} tan	heta & \ = \frac{2 - \frac{1}{2}}{1 + 2\left( \frac{1}{2} ight)} = \frac{3}{4} \ \frac{r}{\sqrt{8^{2} + 4^{2}}} & \ = tan	heta = \frac{3}{4} = \frac{r}{4\sqrt{5}} \ \Rightarrow \ r & \ = 3\sqrt{5} \end{matrix}$$

Question

Options

Solution

More Circle Questions