Determine the radius of the circle, two of whose tangents are the lines 2x+3y-

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Determine the radius of the circle, two of whose tangents are the lines 2x+3y-9 = 0 and 4x+6y+19 =0

Options:

A .

\frac{13}{4 \sqrt{37}}

B .

\frac{35}{4 \sqrt{13}}

C .

\frac{11}{4 \sqrt{13}}

D .

\frac{37}{4 \sqrt{13}}

Answer: Option D
:
D

The given tangents are

2x+3y-9 = 0

4x+6y+19 =0

Or 2x + 3y + $\frac{19}{2}$ = 0

Which are parallel, than distance between parallel tangents must be diameter of the circle than diameter.
$\frac{∣ ∣ ∣ \frac{19}{2} - (- 9) ∣ ∣ ∣}{\sqrt{2^{2} + 3^{2}}} = \frac{37}{2 \sqrt{13}}$

Radius = $\frac{1}{2}$ diameter = $\frac{37}{4 \sqrt{13}}$

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