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Question

# AB and CD are parallel chords on opposite sides of centre of circle. If AB = 10 cm, CD = 24 cm, distance between chords is 17 cm, radius of circle is

A
10 cm
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B
13 cm
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C
15 cm
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Solution

## The correct option is B 13 cm Given: AB and CD are parallel chords on opposite sides of the centre of a circle. Distance between two chords = 17 cm Construction: Draw perpendiculars OE and OF onto AB and CD respectively from centre O. AE = EB = 5 cm and CF = FD = 12 cm [Perpendicular drawn to a chord from the centre bisects the chord] Let distance between O and F =x cm So, distance between O and E =(17−x) cm In ΔOEB, OB2=OE2+EB2 [Pythagoras theorem] =(17−x)2+52 ---(1) In ΔOFD, OD2=OF2+FD2 [Pythagoras theorem] =(x)2+122----------→(2) But OB = OD ( radii of the same circle). From 1 & 2, (17−x)2+52=(x)2+122 ⇒ 289+x2−34x+25=x2+144 ⇒ 34x=170 ∴ x=5 Subsitute x in equation (2); OD2=(5)2+122=169 OD=13 ∴ Radius of the circle is 13 cm.

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