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10-1.Circle and System of Circles
easy
If $2x - 4y = 9$ and $6x - 12y + 7 = 0$ are the tangents of same circle, then its radius will be
A
$\frac{{\sqrt 3 }}{5}$
B
$\frac{{17}}{{6\sqrt 5 }}$
C
$\frac{{2\sqrt 5 }}{3}$
D
$\frac{{17}}{{3\sqrt 5 }}$
Solution
(b) Since the tangents are parallel, therefore the distance between these two tangents will be its diameter
$i.e$., diameter $ = \frac{{34}}{{\sqrt {180} }}$
$= \frac{{17}}{{3\sqrt 5 }}$
Hence, radius $ = \frac{{17}}{{6\sqrt 5 }}$.
Standard 11
Mathematics
