The lines $3 x-4 y+4=0$, and $6 x-8 y-7=0$ are tangents to the same circle. The radius of this circl

Question

The lines $3 x-4 y+4=0$, and $6 x-8 y-7=0$ are tangents to the same circle. The radius of this circle is M/N in the lowest form. Find M+N

Professor PC Thomas Classes · Answer

The given lines $3 x-4 y+4=0$ and $3 x-4 y-\frac{7}{2}=0$ are parallel.\ $	herefore$ Perpendicular distance between the lines\ $=\frac{\left|4-\left(-\frac{7}{2}ight)ight|}{\sqrt{3^{2}+(-4)^{2}}}=\frac{15 / 2}{5}=\frac{3}{2}$\ $	herefore \quad$ Diameter of the circle $=\frac{3}{2}$\ $	herefore \quad$ Radius $=\frac{3}{4}$\