A chord of length 16 cm is at a distance 6 cm from the center of the circle. Find the length of chord of the same circle which is at a distance of 8 cm from the center.

From figure, AB is the chord which is at a distance 6 cm from the center so OC = 6 cm. Since, the perpendicular to a chord from the centre of the circle bisects the chord, ∴ CB = AC = = 8 cm. In right angle triangle OAC, ⇒ OA 2 = OC 2 + AC 2 (By pythagoras theorem) ⇒ OA 2 = 6 2 + 8 2 ⇒ OA 2 = 36 + 64 ⇒ OA 2 = 100 ⇒ OA = = 10 cm. Radius = 10 cm, ∴ OD = 10 cm. From figure, In right angle triangle ODF, ⇒ OD 2 = OF 2 + DF 2 (By pythagoras theorem) ⇒ DF 2 = OD 2 - OF 2 ⇒ DF 2 = 10 2 - 8 2 ⇒ DF 2 = 100 - 64 = 36 ⇒ DF = = 6 cm. Since, the perpendicular to a chord from the centre of the circle bisects the chord ∴ DE = DF + FE = 6 cm + 6 cm = 12 cm. Hence, the length of chord which is at a distance of 8 cm from the center of the circle = 12 cm.

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

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Calculate the length of a chord which is at a distance 6 cm from the center of a circle of diameter 20 cm.

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In a circle of radius 5 cm, AB and CD are two parallel chords of length 8 cm and 6 cm respectively. Calculate the distance between the chords, if they are on
(i) the same side of the centre
(ii) the opposite sides of the centre.

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In figure (i) given below, 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) radius of the circle
(ii) length of chord CD.

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Mathematics

A chord of length 16 cm is at a distance 6 cm from the center of the circle. Find the length of chord of the same circle which is at a distance of 8 cm from the center.

Circles

Related Questions

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

Calculate the length of a chord which is at a distance 6 cm from the center of a circle of diameter 20 cm.

In a circle of radius 5 cm, AB and CD are two parallel chords of length 8 cm and 6 cm respectively. Calculate the distance between the chords, if they are on
(i) the same side of the centre
(ii) the opposite sides of the centre.

In figure (i) given below, 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) radius of the circle
(ii) length of chord CD.

Mathematics

A chord of length 16 cm is at a distance 6 cm from the center of the circle. Find the length of chord of the same circle which is at a distance of 8 cm from the center.

Circles

Related Questions

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

Calculate the length of a chord which is at a distance 6 cm from the center of a circle of diameter 20 cm.

In a circle of radius 5 cm, AB and CD are two parallel chords of length 8 cm and 6 cm respectively. Calculate the distance between the chords, if they are on(i) the same side of the centre(ii) the opposite sides of the centre.

In figure (i) given below, 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) radius of the circle(ii) length of chord CD.

In a circle of radius 5 cm, AB and CD are two parallel chords of length 8 cm and 6 cm respectively. Calculate the distance between the chords, if they are on
(i) the same side of the centre
(ii) the opposite sides of the centre.

In figure (i) given below, 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) radius of the circle
(ii) length of chord CD.