Q. 214.0( 5 Votes )

AB and CD are two parallel chords of a circle with centre O such that AB=6 cm and CD= 12 cm. The chords are on the same side of the centre and the distance between them in 3 cm. The radius of the circle is
A. 6 cm

B. 5 cm

C. 7 cm

D. 3 cm

Answer :

Given that,

AB || CD (Chords on same side of centre)


AO = CO (Radii)


OL and OM perpendicular bisector of CD and AB respectively


CL = LD = 6 cm


AM = MB = 3 cm


LM = 3 cm (Given)


In COL,


CO2 = OL2 + 62 (i)


In AOM,


AO2 = AM2 + OM2


= 2 + (OL + LM)2


= 9 + OL2 + 9 + 6O L


OL2 = AO2 - 18 - 6O L (ii)


Using (ii) in (i),


OL = 3 cm


Putting OL in (i),


AO2 =


AO = 35

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