Two parallel chords of lengths 80 cm and 18 cm are drawn on the same side of the centre of a circle of radius 41 cm. Find the distance between the chords.
Circles
2 Likes

Question

Two parallel chords of lengths 80 cm and 18 cm are drawn on the same side of the centre of a circle of radius 41 cm. Find the distance between the chords.

KnowledgeBoat · Accepted Answer

Let AB = 18 cm and CD = 80 cm be chords on same side of the center of the circle. OE CD and OF AB We know that, Perpendicular from the center to the chord, bisects it. ∴ AF = = 9 cm. CE = = 40 cm. From figure, OA = OC = radius = 41 cm. In right-angled triangle OCE, By pythagoras theorem, ⇒ Hypotenuse2 = Perpendicular2 + Base2 ⇒ OC2 = OE2 + CE2 ⇒ 412 = OE2 + 402 ⇒ 1681 = OE2 + 1600 ⇒ OE2 = 1681 - 1600 ⇒ OE2 = 81 ⇒ OE = = 9 cm. In right-angled triangle OAF, By pythagoras theorem, ⇒ Hypotenuse2 = Perpendicular2 + Base2 ⇒ OA2 = OF2 + AF2 ⇒ 412 = OF2 + 92 ⇒ 1681 = OF2 + 81 ⇒ OF2 = 1681 - 81 ⇒ OF2 = 1600 ⇒ OF = = 40 cm. From figure, ⇒ EF = OF - OE = 40 - 9 = 31 cm. Hence, distance between the chords = 31 cm.

Mathematics

Two parallel chords of lengths 80 cm and 18 cm are drawn on the same side of the centre of a circle of radius 41 cm. Find the distance between the chords.

Circles

Related Questions

A chord of length 16 cm is at a distance of 15 cm from centre of the circle. Find the length of chord of same circle which is at 8 cm away from circle.

Two parallel chords of lengths of 30 cm and 16 cm are drawn on the opposite sides of the centre of a circle of radius 17 cm. Find the distance between chords.

Two parallel chords AB and CD are 3.9 cm apart and lie on the opposite sides of the centre of a circle. If AB = 1.4 cm and CD = 4 cm, find the radius of the circle.

AB and CD are two parallel chords of lengths 8 cm and 6 cm respectively. If they are 1 cm apart and lie on the same side of the centre of the circle, find the radius of the circle.