If the center of a circle is the point (3, 4) and it touches the line 3x + 4y - 5 = 0, then find the radius of circle.

Concept:

The distance between a point P(x₁, y₁) and the line ax + by + c = 0 is given by:

Distance = \(\rm \dfrac{|ax_1+by_1+c|}{\sqrt{a^2+b^2}}\).

Calculation:

Since the circle touches the line at a point, the radius of the circle will be the distance between the center of the circle and the given line.

Using the formula for the distance between a point (3, 4) and a line (3x + 4y - 5 = 0), we get:

Radius = \(\rm \dfrac{|3(3)+4(4)-5|}{\sqrt{3^2+4^2}}\) = \(\rm \dfrac{20}{5}\) = 4.