1.

11. If the lines \( 5 x+12 y=3 \) and \( 10 x+24 y-58=0 \) are tangents to a circle, then find the radius of the circle.

Answer»

Given tangents are-

5x + 12y = 3 ...(i)

5x + 12y = 29...(ii)

The tangents are parallel in this case.

Now, the chord formed by two parallel tangents of a circle is the diameter of the circle.

\(d = |\frac{c_{2}-{c_{1}}}{\sqrt{a²+b²}}|\\d=|\frac{-29+3}{5²+12²}|\\d=|\frac{-26}{13}| \\d=2\)

Now, d =2r 

r = 1 unit



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