Question

The radius of a circle is 6 cm. The perpendicular distance from the centre of the circle to the chord which is 8 cm in length, is

• A. $\sqrt{5}cm$
• B. $2\sqrt{5}cm$
• C. $2\sqrt{7}cm$
• D. $\sqrt{7}cm$

Answer 1

The correct option is B

$2\sqrt{5}cm$

Radius of the circle (r) = 6 cm

Perpendicular distance from centre = ?

Length of chord = 8 cm

Let AB be chord, OL is the perpendicular distance.

In right $\Delta OAL$, $O{A}^2=A{L}^2+O{L}^2$

$\Rightarrow (6{)}^2={\left(\frac{8}{2}\right)}^2+O{L}^2\{\because AL=\frac{1}{2}AB\}$

$\Rightarrow 36=16+O{L}^2\Rightarrow O{L}^2=36-16=20$

$\therefore OL=\sqrt{20}=\sqrt{4\times 5}=2\sqrt{5}cm$