What is the easiest way for solving the question of class 9th ncert math of exercise 10.6of math of Circles chapter of question no. 2 Please help me for the best suggestion of this question Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 , find the radius of the circle.
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Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 , find the radius of the circle. Q.2
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Here, OM ⊥ AB and ON ⊥ CD. is drawn and OB and OD are joined.
We know that AB bisects 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
Or,
Consider ΔNOD,
OD2 = ON2 + ND2
Or
We know, OB = OD (radii)
From equation 1 and equation 2 we get
Now, from equation (2) we have,
OD2= 12 +(121/4)
Or OD = (5/2)×√5 cm