The Total solution for NCERT class 6-12
Two chords AB and CD of lengths 5 cm and 11 cm respectively of acircle are parallel to each other and are on opposite sides of its centre. Ifthe distance between AB and CD is 6 , find the radius of the circle.
Here, OM ⊥ AB and ON ⊥ CD. is drawn and OB and OD are joined.
We know that ABbisects BM as the perpendicular from the centre bisects chord.
Since AB = 5 so,
BM = AB/2
Similarly, ND = CD/2 =11/2
Now, let ON be x.
So, OM = 6−x.
Consider ΔMOB,
OB2 =OM2+MB2
Consider ΔNOD,
OD2 =ON2 + ND2
Or
We know, OB = OD(radii)
From equation 1 andequation 2 we get
Now, from equation (2)we have,
OD2= 12 +(121/4)
Or OD = (5/2)×√5 cm