If the length of the chord of the circle, x2 + y2 = r2 (r 0) along the line, y -- 2x = 3…

Question

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 60o = $${{CD} \over r}$$

$$ \Rightarrow $$ 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 = $${{12} \over 5}$$

Solutions · 1