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17, Tvo parallel chords of a circle, 12 cm and 16 cm long are on the same side of the centre. The distancebetween them is 2 cm. Find the radius of the circle |
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Answer» Given chords AB=12 cm, CD =16 cm and AB||CDDraw OP⊥ AB. Let it intersect CD at Q and AB at P∴ AP = PB = 6 cm and CQ = DQ = 8 cm [Since perpendicular draw from the centre of the chord bisects the chord]Let OD = OB = rIn right ΔOQD, r^2 = x^2 + 8^2 [By Pythagoras theorem]r^2 = x^2 + 64 → (1) In right ΔOPB, r^2 = (x + 2)^2 + 6^2 [By Pythagoras theorem]Þ r^2 = x^2 + 4x + 4 + 36 = x^2 + 4x + 40 → (2) From (1) and (2) we getx^2 + 64 = x^2 + 4x + 40⇒ 4x = 24∴ x = 6 therefore radius of circle is 6cm.Put x = 3 in (1), we getr2 = 32 + 36 = 9 + 36 = 45∴ r = √45 = 3√5 cm |
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