In the adjoining figure, AB and CD are two parallel chords and O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of length 24 cm and 18 cm respectively.

In the figure, chords AB ∥ CD and O is the centre of the circle. Radius of the circle = 15 cm Length of AB = 24 cm and CD = 18 cm. Join OA and OC. AB = 24 cm and OM ⊥ AB. ∴ AM = MB = = 12 cm (As perpendicular to a chord from the center of the circle bisects it) In right angle triangle OAM, ⇒ OA 2 = OM 2 + AM 2 (By pythagoras theorem) ⇒ OM 2 = OA 2 - AM 2 ⇒ OM 2 = 15 2 - 12 2 ⇒ OM 2 = 225 - 144 ⇒ OM 2 = 81 ⇒ OM = = 9 cm. Similarly ON ⊥ CD CN = ND = = 9 cm Similarly In right ∆CNO, ⇒ OC 2 = ON 2 + CN 2 (By pythagoras theorem) ⇒ ON 2 = OC 2 - CN 2 ⇒ ON 2 = 15 2 - 9 2 ⇒ ON 2 = 225 - 81 ⇒ ON 2 = 144 ⇒ ON = = 12 cm. MN = OM + ON = 9 + 12 = 21 cm. Hence, MN = 21 cm.

AB and CD are two parallel chords of a circle of lengths 10 cm and 4 cm respectively. If the chords lie on the same side of the centre and the distance between them is 3 cm, find the diameter of the circle.

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In the figure (ii) given below, CD is the diameter which meets the chord AB in E such that AE = BE = 4 cm. If CE = 3 cm, find the radius of the circle.

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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

In the adjoining figure, AB and CD are two parallel chords and O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of length 24 cm and 18 cm respectively.

Circles

Related Questions

AB and CD are two parallel chords of a circle of lengths 10 cm and 4 cm respectively. If the chords lie on the same side of the centre and the distance between them is 3 cm, find the diameter of the circle.

In the figure (ii) given below, CD is the diameter which meets the chord AB in E such that AE = BE = 4 cm. If CE = 3 cm, find the radius of the circle.

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

In the adjoining figure, AB and CD are two parallel chords and O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of length 24 cm and 18 cm respectively.

Circles

Related Questions

AB and CD are two parallel chords of a circle of lengths 10 cm and 4 cm respectively. If the chords lie on the same side of the centre and the distance between them is 3 cm, find the diameter of the circle.

In the figure (ii) given below, CD is the diameter which meets the chord AB in E such that AE = BE = 4 cm. If CE = 3 cm, find the radius of the circle.

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 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.