QJEEM20Maa888: JEE Main 2020 Mathematics - Class 11 JEEM20Maa888 Solution: If the length of the chord of the circle, x 2 + y 2 = r 2 (r >…

Question

Verified Solution • 2025–26 Session moderate

If the length of the chord of the circle,
x² + y² = r² (r > 0) along the line, y – 2x = 3 is r,
then r² is equal to :

Accepted Answer

In right

\Delta

CDB,

sin 60^o =

{{CD} \over r}

\Rightarrow

CD =

r \times {{\sqrt 3 } \over 2}

=

{{\sqrt 3 r} \over 2}

Now equation of AB is

y – 2x – 3 = 0

So

{{\sqrt 3 r} \over 2}

=

{{\left| {0 + 0 - 3} \right|} \over {\sqrt 5 }}

\Rightarrow

{{\sqrt 3 r} \over 2}

=

{3 \over {\sqrt 5 }}

\Rightarrow

r =

{{2\sqrt 3 } \over 5}

\Rightarrow

r² =

{{12} \over 5}

Step-by-Step Verified Solution