Question

The radius of a circle is 8 cm and the length of one of its chords is 12 cm. Find the distance of the chord from the centre.

Answer 1

Radius of circle with centre O is OA = 8 cm Length of chord AB = 12 cm

OL $\perp$ AB which bisects AB at L.

$\therefore AL=LB=12\times \frac{1}{2}=6cm$

In $\Delta OAL$,

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

$\Rightarrow (8{)}^2=O{L}^2+(6{)}^2$

$\Rightarrow 64=O{L}^2+36\Rightarrow O{L}^2=64-36=28$

$\therefore OL=\sqrt{28}=\sqrt{4\times 7}cm$

$=2\times 2.6457=5.291cm$