Question

The diameter of a circle is 30 and the length of a chord in this circle is 24. Find the distance of thatchord from the centre. (with diagram) ​

Answer 1

$\textrm{The Diameter of Circle is 30 cm, So Radius = 15 cm ( \because Radius = Diameter \div 2)}$

$\longrightarrow\textrm{ Let Radius of Circle be OA. So OA = 15 cm}$

$\longrightarrow\textrm{ Let the Length of the chord be AB. So AB = 24 cm}$

$\longrightarrow\textrm{ Let C be the midpoint of AB. So AC = CB = 12 cm}$

$\bigstar\textrm{ In \triangle AOC, \angle C = 90 ^\circ (Right Angle) }$

$\longrightarrow\textrm{ OA ^2 = AC ^2 + OC ^2\quad ....From Pythagoras Theorem}$

$\longrightarrow\textrm{ (15 cm) ^2 = (12 cm) ^2 + OC ^2 }$

$\longrightarrow\textrm{ 225 cm ^2 = 144 cm ^2 + OC ^2 }$

$\longrightarrow\textrm{ OC ^2 = 225 cm ^2 - 144 cm ^2 = 81 cm ^2 }$

$\longrightarrow\textrm{ OC = \sqrt{\rm{81 cm^2}} = 9 cm}$

$\underline{\underline{\textrm{ \therefore Distance of Chord from Center is 9 cm}}}$