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.

Question

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.

KnowledgeBoat · Accepted Answer

(i) From figure, AB and CD are chords of length 8 cm and 6 cm, respectively. Since, the perpendicular to a chord from the centre of the circle bisects the chord, ∴ AE = BE = = 4 cm and, CF = FD = = 3 cm. Radius = OA = OC = 5 cm. In right angle triangle OAE, ⇒ OA² = AE² + OE² (By pythagoras theorem) ⇒ OE² = OA² - AE² ⇒ OE² = 5² - 4² ⇒ OE² = 25 - 16 = 9 ⇒ OE = = 3 cm. In right angle triangle OCF, ⇒ OC² = CF² + OF² (By pythagoras theorem) ⇒ OF² = OC² - CF² ⇒ OF² = 5² - 3² ⇒ OF² = 25 - 9 = 16 ⇒ OF = = 4 cm. Distance between two chords = EF = OF - OE = 4 - 3 = 1 cm. Hence, distance between two chords = 1 cm. (ii) From figure, AB and CD are chords of length 8 cm and 6 cm respectively. Since, the perpendicular to a chord from the centre of the circle bisects the chord, ∴ AE = BE = = 4 cm and, CF = FD = = 3 cm. Radius = OA = OC = 5 cm. In right angle triangle OAE, ⇒ OA² = AE² + OE² (By pythagoras theorem) ⇒ OE² = OA² - AE² ⇒ OE² = 5² - 4² ⇒ OE² = 25 - 16 = 9 ⇒ OE = = 3 cm. In right angle triangle OCF, ⇒ OC² = CF² + OF² (By pythagoras theorem) ⇒ OF² = OC² - CF² ⇒ OF² = 5² - 3² ⇒ OF² = 25 - 9 = 16 ⇒ OF = = 4 cm. Distance between two chords = EF = OF + OE = 4 + 3 = 7 cm. Hence, distance between two chords = 7 cm.

Mathematics

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.

Circles

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(i) radius of the circle
(ii) length of chord CD.

Mathematics

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.

Circles

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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.

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.