Question

In the given figure, O is the center of the circle. AB and CD are two chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD. AB = 24 cm, OM = 5 cm, ON = 12 cm,

Find the :
(i) the radius of the circle
(ii) length of chord CD.

Answer 1

(i) AB is the chord of the circle and OM is perpendicular to AB.
So, AM = MB = 12 cm ....( Since ⊥ bisects the chord )
In right ΔOMA,
OA² = OM² + AM²
⇒ OA² = 5² + 12^2
⇒  OA = 13 cm
So, radius of the circle is 13 cm.

(ii) So, OA = OC = 13 cm  ....( radii of the same circle )
In right ΔONC,
NC² = OC² - ON²
⇒ NC² = 13² - 12²
⇒ NC = 5 cm
So, CD = 2NC = 10 cm.