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10-1.Circle and System of Circles
easy
જો રેખાઓ $3x - 4y + 4 = 0$ અને $6x - 8y - 7 = 0$ વર્તૂળના સ્પર્શકો હોય તો તેની ત્રિજયા મેળવો.
A
$3\over2$
B
$3\over4$
C
$1\over10 $
D
$1\over20$
(IIT-1984)
Solution
(b) The diameter of the circle is perpendicular distance between the parallel lines $(tangents)$ $3x – 4y + 4 = 0$ and $3x – 4y – \frac{7}{2} = 0$ and so it is equal to $\frac{4}{{\sqrt {9 + 16} }} + \frac{{7/2}}{{\sqrt {9 + 16} }} = \frac{3}{2}$.
Hence radius is $\frac{3}{4}$.
Standard 11
Mathematics
