Question

AB and CD are two parallel chords of a circle such that AB$=24$cm and CD$=10$cm. If the radius of the circle is $13$cm, find the distance between the two chords.

Answer 1

Given

$\Delta$ ANO is a right angle triangle,

$\therefore$ using pythogoras theorem,

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

${13}^2=O{N}^2+{12}^2$

$O{N}^2={13}^2-{12}^2=169-144$

$O{N}^2=25$

$\Rightarrow O{N}^2=5cm$

Similarly for $\Delta$OCM

$O{C}^2=O{M}^2+C{M}^2$

${13}^2=O{M}^2+5^2$

$O{M}^2={13}^2-5^2$

$O{M}^2=169-25$

$OM=\sqrt{144}$

$=12cm$

$\therefore$ Distance between chorts

$=OM+ON$

$=12+5$

$=17$cm.

Thus the distance between the two chords is $17$cm.