If the length of the chord of the circle, x 2 + y 2 = r 2 ( r > 0 ) along the line, y - 2 x = 3 is r , then r 2 is equal to:

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Question: Answered & Verified by Expert

If the length of the chord of the circle,

x^{2} + y^{2} = r^{2} (r > 0)

along the line,

y - 2 x = 3

is

r

, then

r^{2}

is equal to:

MathematicsCircleJEE MainJEE Main 2020 (05 Sep Shift 2)

Options:

A $\frac{9}{5}$
B $12$
C $\frac{24}{5}$
D $\frac{12}{5}$

Solution:

1528 Upvotes Verified Answer

The correct answer is:

\frac{12}{5}

$A B = r, A D = \frac{r}{2}$

$CD = rsin 60 ° = \frac{\sqrt{3} r}{2}$
$\Rightarrow \frac{|0 + 0 - 3|}{\sqrt{1^{2} + 2^{2}}} = \frac{\sqrt{3} r}{2} \Rightarrow r = 2 \sqrt{\frac{3}{5}} \Rightarrow r^{2} = \frac{12}{5}$

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