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.

Let OE = x cm. From figure, In right angle triangle OCF, ⇒ OC 2 = OF 2 + CF 2 (By pythagoras theorem) ⇒ OC 2 = (x + 3) 2 + 2 2 ⇒ OC 2 = x 2 + 9 + 6x + 4 ⇒ OC 2 = x 2 + 6x + 13 Since, radius = OA = OC. ∴ OA 2 = OC 2 = x 2 + 6x + 13. In right angle triangle OAE, ⇒ OA 2 = OE 2 + AE 2 ⇒ x 2 + 6x + 13 = x 2 + 5 2 ⇒ x 2 - x 2 + 6x = 25 - 13 ⇒ 6x = 12 ⇒ x = = 2 cm. ⇒ OC 2 = x 2 + 6x + 13 ⇒ OC 2 = 2 2 + 6(2) + 13 ⇒ OC 2 = 4 + 12 + 13 ⇒ OC 2 = 29 ⇒ OC = cm. Diameter = 2 × radius = 2 × cm. Hence, diameter = cm.

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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An equilateral triangle of side 6 cm is inscribed in a circle. Find the radius of the circle.

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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.

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Mathematics

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.

Circles

Related Questions

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.

An equilateral triangle of side 6 cm is inscribed in a circle. Find the radius of the circle.

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.