iran-konkur 2021 Q154

iran-konkur · Other · konkur-riazi_1400_specialized Circles Distance from Center to Line
154. Suppose lines $x + y = 1$ and $x - y = 3$ are the diameters of a circle, and the line $4x + 3y + 5 = 0$ is tangent to it. What is the distance of point $M(4, -2)$ from the circle?
  • [(1)] $\sqrt{3} - 1$
  • [(2)] $\sqrt{3} - \sqrt{2}$
  • [(3)] $\dfrac{\sqrt{7}}{2}$
  • [(4)] $\sqrt{5} - 2$

\textbf{154.} Suppose lines $x + y = 1$ and $x - y = 3$ are the diameters of a circle, and the line $4x + 3y + 5 = 0$ is tangent to it. What is the distance of point $M(4, -2)$ from the circle?

\begin{itemize}
    \item[(1)] $\sqrt{3} - 1$
    \item[(2)] $\sqrt{3} - \sqrt{2}$
    \item[(3)] $\dfrac{\sqrt{7}}{2}$
    \item[(4)] $\sqrt{5} - 2$
\end{itemize}

\vspace{0.5cm}