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.

Question

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.

KnowledgeBoat · Accepted Answer

(i) Let AB and CD be chords on opposite side of the center of the circle. We know that, Perpendicular from the center to the chord, bisects it. ∴ AF = = 8 cm, CE = = 15 cm. From figure, OA = OC = radius = 17 cm. In right-angled triangle OCE, By pythagoras theorem, ⇒ Hypotenuse² = Perpendicular² + Base² ⇒ OC² = OE² + CE² ⇒ 17² = OE² + 15² ⇒ 289 = OE² + 225 ⇒ OE² = 289 - 225 ⇒ OE² = 64 ⇒ OE = = 8 cm. In right-angled triangle OAF, By pythagoras theorem, ⇒ Hypotenuse² = Perpendicular² + Base² ⇒ OA² = OF² + AF² ⇒ 17² = OF² + 8² ⇒ 289 = OF² + 64 ⇒ OF² = 289 - 64 ⇒ OF² = 225 ⇒ OF = = 15 cm. From figure, ⇒ EF = OE + OF = 8 + 15 = 23 cm. Hence, distance between the chords = 23 cm. (ii) Let AB and CD be chords on same side of the center of the circle. We know that, Perpendicular from the center to the chord, bisects it. ∴ AF = = 8 cm, CE = = 15 cm. From figure, OA = OC = radius = 17 cm. In right-angled triangle OCE, By pythagoras theorem, ⇒ Hypotenuse² = Perpendicular² + Base² ⇒ OC² = OE² + CE² ⇒ 17² = OE² + 15² ⇒ 289 = OE² + 225 ⇒ OE² = 289 - 225 ⇒ OE² = 64 ⇒ OE = = 8 cm. In right-angled triangle OAF, By pythagoras theorem, ⇒ Hypotenuse² = Perpendicular² + Base² ⇒ OA² = OF² + AF² ⇒ 17² = OF² + 8² ⇒ 289 = OF² + 64 ⇒ OF² = 289 - 64 ⇒ OF² = 225 ⇒ OF = = 15 cm. From figure, ⇒ EF = OF - OE = 15 - 8 = 7 cm. Hence, distance between the chords = 7 cm.

Mathematics

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.

Circles

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Mathematics

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.

Circles

Related Questions

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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.

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Given OA = OB = 15 cm and OP = 9 cm. Calculate the lengths of :
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