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.
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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.

KnowledgeBoat · Accepted Answer

AB = 8 cm and CD = 6 cm OF AB and OE CD We know that, Perpendicular from the center to the chord, bisects it. ∴ AF = = 4 cm. CE = = 3 cm. EF = 1 cm and OA = OC = r cm. Let OF = x and OE = x + 1 In right-angled triangle OCE, By pythagoras theorem, ⇒ Hypotenuse2 = Perpendicular2 + Base2 ⇒ OC2 = OE2 + CE2 ⇒ r2 = (x + 1)2 + 32 ⇒ r2 = (x + 1)2 + 9 .....(1) In right-angled triangle OAF, By pythagoras theorem, ⇒ Hypotenuse2 = Perpendicular2 + Base2 ⇒ OA2 = OF2 + AF2 ⇒ r2 = x2 + 42 ⇒ r2 = x2 + 16 ....(2) From (1) and (2), ⇒ x2 + 16 = (x + 1)2 + 9 ⇒ x2 + 16 = x2 + 2x + 1 + 9 ⇒ x2 + 16 = x2 + 2x + 10 ⇒ 16 = 2x + 10 ⇒ 2x = 16 - 10 ⇒ 2x = 6 ⇒ x = ⇒ x = 3. Substituting value of x in equation (2), we get : ⇒ r2 = 32 + 16 ⇒ r2 = 9 + 16 ⇒ r2 = 25 ⇒ r = = 5 cm. Hence, radius of the circle = 5 cm.

Mathematics

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.

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