Question

A chord of length 6 cm is drawn on a circle of radius 5 cm. Calculate its distance from the centre of the circle.

Answer 1

In the circle shown above, O is the centre.

Radius, OA = 5 cm

Chord AB = 6 cm

OM $\perp$ AB, which bisects it at M.

$\therefore AM=\frac{1}{2}AB=\frac{1}{2}\times 6\text{cm}=3\text{cm}$

Now, in right $\Delta OMA$,

$O{A}^2=A{M}^2+O{M}^2$ (Pythagoras' Theorem)

$\Rightarrow (5{)}^2=(3{)}^2+O{M}^2$

$\Rightarrow 25=9+O{M}^2\Rightarrow O{M}^2=25-9=16$

$\therefore OM=\sqrt{16}=4cm$