Question

A chord of length 12cm is at a distance of 3cm from the centre of a circle. then its radius is

• A. $2\sqrt{5}$cm
• B. $3\sqrt{5}$cm
• C. $4\sqrt{5}$cm
• D. $6\sqrt{5}$cm

Answer 1

The correct option is B $3\sqrt{5}$cm

AM is chord of length $12$cm

Distance of chord from centre of circle is $3$cm

$\therefore$As OB is perpendicular to AM

$AB=\frac{AM}{2}=\frac{12}{2}=6cm$

$\therefore$ Using Pythagoras theorem

$A{B}^2+O{B}^2=O{A}^2$

$\therefore O{A}^2=6^2+3^2$

$O{A}^2=36+9$

$O{A}^2=45$

$OA=\sqrt{45}$

$=\sqrt{5\times 3\times 3}$

$=3\sqrt{5}cm$.