A chord of length 24 cm is at a distance of 5 cm from the center of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the centre.

Let AB be the chord of the circle with center O at the distance of 5 cm from the center of the circle. We know that, Perpendicular from center to chord, bisects the chord. ∴ AC = = 12 cm. In right angled triangle OAC, By pythagoras theorem, ⇒ Hypotenuse 2 = Perpendicular 2 + Base 2 ⇒ OA 2 = OC 2 + AC 2 ⇒ OA 2 = 5 2 + 12 2 ⇒ OA 2 = 25 + 144 ⇒ OA 2 = 169 ⇒ OA = = 13 cm. From figure, OD = OA = 13 cm (Radius of same circle) Let chord DE be at the distance of 12 cm from the center. In right angled triangle OFD, By pythagoras theorem, ⇒ Hypotenuse 2 = Perpendicular 2 + Base 2 ⇒ OD 2 = OF 2 + FD 2 ⇒ 13 2 = 12 2 + FD 2 ⇒ FD 2 = 13 2 - 12 2 ⇒ FD 2 = 169 - 144 ⇒ FD 2 = 25 ⇒ FD = = 5 cm. ⇒ DE = 2 × FD = 2 × 5 = 10 cm. Hence, length of chord at a distance of 12 cm from the centre equals to 10 cm.

A chord of length 8 cm is drawn at a distance of 3 cm from the center of a circle. Calculate the radius of the circle.

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In the following figure, AD is a straight line. OP ⊥ AD and O is the centre of both the circles. If OA = 34 cm, OB = 20 cm and OP = 16 cm; find the length of AB.

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Mathematics

A chord of length 24 cm is at a distance of 5 cm from the center of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the centre.

Circles

Related Questions

A chord of length 8 cm is drawn at a distance of 3 cm from the center of a circle. Calculate the radius of the circle.

The radius of a circle is 17.0 cm and the length of perpendicular drawn from its center to a chord is 8.0 cm. Calculate the length of the chord.

In the following figure, AD is a straight line. OP ⊥ AD and O is the centre of both the circles. If OA = 34 cm, OB = 20 cm and OP = 16 cm; find the length of AB.

In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. Find the distance between the chords, if both the chords are :
(i) on the opposite sides of the center,
(ii) on the same side of the center.

Mathematics

A chord of length 24 cm is at a distance of 5 cm from the center of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the centre.

Circles

Related Questions

A chord of length 8 cm is drawn at a distance of 3 cm from the center of a circle. Calculate the radius of the circle.

The radius of a circle is 17.0 cm and the length of perpendicular drawn from its center to a chord is 8.0 cm. Calculate the length of the chord.

In the following figure, AD is a straight line. OP ⊥ AD and O is the centre of both the circles. If OA = 34 cm, OB = 20 cm and OP = 16 cm; find the length of AB.

In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. Find the distance between the chords, if both the chords are :(i) on the opposite sides of the center,(ii) on the same side of the center.

In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. Find the distance between the chords, if both the chords are :
(i) on the opposite sides of the center,
(ii) on the same side of the center.