Q. 35.0( 5 Votes )

Two chords AB and

Answer :


Given chords AB = 6 cm and CD = 12 cm,


Draw OE AB intersecting CD at F,


As, AB||CD


OF CD [Corresponding angles]


Distance between AB and CD, EF= 3 cm


Now, we know that perpendicular from center to chord bisects the chord.


Then CF = FD = 1/2 CD = 6 cm


AE = EB = 1/2 AB = 3 cm


Let OF = y cm, OE = 3 + y cm and OD = OB = x cm = Radius.


Consider ΔOFD,


By Pythagoras Theorem,


OD2 = OF2 + FD2


x2 = y2 + 62


x2 = y2 + 36 … (1)


Consider ΔOEB,


By Pythagoras Theorem,


OB2 = OE2 + EB2


x2 = (3 + y)2 + 32


x2 = 9 + y2 + 6y + 9


x2 = y2 + 6y + 18 … (2)


From (1) and (2),


y2 + 36 = y2 + 6y + 18


36 = 6y + 18


6y = 36 – 18


6y = 18


y = 18/ 6


y = 3


Substituting y value in (1),


x2 = y2 + 36


x2 = 32 + 36


x2 = 9 + 36


x2 = 45


[45 = 3 × 3 × 5]


Radius = x = 3√5 cm


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