Q2 of 141 Page 400

Find the length of a chord which is at a distance of 3 cm from the center of a circle of radius 5 cm.


Let distance OC = 3 cm


Radius = OA = 5 cm


Draw OCAB


In triangle OCA,


OA2 = OC2 + AC2


⇒ 52 = 32 + AC2


⇒ AC2= 16


⇒ AC = 4 cm __________________ (i)


Now,


AB = 2 AC


⇒ AB = 8 cm [From equation (i)]


Hence, length of a chord = 8 cm.


More from this chapter

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1

A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the center of the circle.

 3

A chord of a length 30 cm is drawn at a distance of 8 cm from the center of a circle. Find out the radius of the circle.

 4

In a circle of radius 5 cm, and are two parallel chords of lengths 8 cm and 6 cm respectively. calculate the distance between the chords if they are

(i) on the same side of the center


(ii) on the opposite sides of the center.

 5

Two parallel chords of lengths 30 cm and 16cm are drawn on the opposite sides of the center of a circle of radius 17 cm. Find the distance between the chords.