First slide

Definition of a circle

Question

The lines $3 x - 4 y + 4 = 0$ and $6 x - B y - 7 = 0$ are tangents to the same circle. Then, its radius, is

Moderate

A

$1 / 4$
B

$1 / 2$
C

$3 / 4$
D

none of these

Solution

Two given tangents are parallel to each other. Therefore, the distance between them is equal to the diameter of the circle.
$∴$ Radius $= \frac{1}{2} \times \{\begin{aligned} Distance between 3 x - 4 y + 4 = 0 \\ and 6 x - 8 y - 7 = 0 \end{aligned}\}$
$\Rightarrow$ Radius $= \frac{1}{2} |\begin{matrix} 4 + \frac{7}{2} \\ \sqrt{9 + 16} \end{matrix}| = \frac{3}{4}$

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