Question

If $AB$ and $AC$ are two chords of a circle of radius $5$ cm such that $AB=AC=4\sqrt{5}$ cm, then the length of the chord $BC$ is

• A. $8$ cm
• B. $8.4$ cm
• C. $9$ cm
• D. None of these

Answer 1

Answer: (A)

$8$ cm

Let $OM=x$.
Then, $x^2+{\left(\frac{11}{2}\right)}^2=r^2$
and $(x+3{)}^2+{\left(\frac{5}{2}\right)}^2=r^2$
Theb, $x^2+6x+9+\frac{25}{4}=x^2+\frac{121}{4}$
$\Rightarrow 6x=15$
$\Rightarrow x=2.5cm$
Thus, $r^2=(2.5{)}^2+\frac{121}{4}=\frac{146}{4}$
$\Rightarrow r=\frac{\sqrt{146}}{2}cm$