Question

If the lines \( 3x - 4y + 4 = 0 \) and \( 6x - 8y - 7 = 0 \) are tangents to a circle, then radius of the circle is:

• A. \( \frac{3}{4} \)
• B. \( \frac{2}{3} \)
• C. \( \frac{1}{4} \)
• D. \( \frac{5}{2} \)

Hint:

The radius of the circle inscribed between two tangents is related to the distance between the tangents.

Answer 1

The Correct Option is C

The radius of the circle is given by the formula \( r = \frac{D}{2} \), where \( D \) is the distance between the two parallel tangents. By calculating the distance between the two lines, we get the radius.
Final Answer: \[ \boxed{\frac{1}{4}} \]