Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 13 cm.

0 votes
1 view
asked Mar 9 in Class X Maths by navnit40 (-3,330 points)

Find the length of a chord which is at a distance of  5 cm from the centre of a circle of radius 13 cm.

Please log in or register to answer this question.

1 Answer

0 votes
answered Mar 9 by aditya23 (-1,379 points)

Let AB be a chord of a circle with centre O and radius 13 cm. Draw OL ⊥ AB.

Join OA. Clearly,  OL = 5 cm and OA = 13 cm.

In the right triangle OLA, we have

OA2 = OL2 + AL2

⇒   132 = 52 + AL2

⇒ AL2 = 144 cm2

⇒ AL = 12 cm

Since, the perpendicular from the centre to the chord bisects the chord. Therefore,

AB = 2AL = (2 × 12) cm

= 24 cm.

Let AB be a chord of a circle with centre O and radius 13 cm. Draw OL ⊥ AB.

Join OA. Clearly,  OL = 5 cm and OA = 13 cm.

In the right triangle OLA, we have

OA2 = OL2 + AL2

⇒   132 = 52 + AL2

⇒ AL2 = 144 cm2

⇒ AL = 12 cm

Since, the perpendicular from the centre to the chord bisects the chord. Therefore,

AB = 2AL = (2 × 12) cm

= 24 cm.

Related questions

...