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
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
= ౩2 + (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