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Question

The straight line x+2y=1 meets the coordinate axes at A and B. A circle is drawn through A,B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is :

A
45
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B
54
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C
25
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D
52
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Solution

The correct option is D 52

Given line AB is x+2y=1
Slope of line AB=12
Co-ordinates of A and B are A=(1,0),B=(0,12)
Co-ordinates of C=⎜ ⎜ ⎜1+02,0+122⎟ ⎟ ⎟=(12,14)
Slope of OC=014012=12

Slope of tangent =2
So, the equation of tangent is 2x+y=0
Sum of distances from A(1,0) and B(0,12) of tangent
=∣ ∣222+12∣ ∣+∣ ∣ ∣1222+12∣ ∣ ∣=25+125=525=52

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