Question

PQuite and RS are two parallel chords of a circle such that AB =12cmy and CD =16cm if chords are on opposite sides of the centre of the circle and distance between them is 16cm find the radius of the circle

Answer 1

Given chords AB=6 cm, CD =12 cm and AB||CD Draw OP⊥ AB. Let it intersect CD at Q and AB at P ∴ AP = PB = 3 cm and CQ = DQ = 6 cm [Since perpendicular draw from the centre of the chord bisects the chord] Let OD = OB = r In right ΔOQD, r2 = x2 + 62 [By Pythagoras theorem]r2 = x2 + 36 → (1) In right ΔOPB, r2 = (x + 3)2 + 32 [By Pythagoras theorem] Þ r2 = x2 + 6x + 9 + 9 = x2 + 6x + 18 → (2) From (1) and (2) we get x2 + 36 = x2 + 6x + 18 ⇒ 6x = 18∴ x = 3 Put x = 3 in (1), we get r2 = 32+ 36 = 9 + 36 = 45 ∴ r = √45 = 3√5 cm

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