Question

Find the length of a chord which is at the distance of 12 cm from the center of a circle of radius 13cm ? ​

Answer 1

Answer:

Let AB be a chord of circle with centre O and radius 13cm. Draw OM perpendicular AB and join OA.

In the right triangle OMA, we have

OA2 = OM2 + AM2

⇒ 132 = 122 + AM2

⇒ AM2 = 169 - 144 = 25 ⇒ AM = 5cm.

As the perpendicular from the centre of a chord bisects the chord.Therefore,

AB = 2AM = 2 x 5 = 10cm.