Question 1
If Radii of two concentric circles are 4 cm and 5 cm, then length of each chord of one circle which is tangent to the other circle, is
(A) 3 cm
(B) 6 cm
(C) 9 cm
(D) 1 cm
Let O be the centre of two concentric circles C1 and C2, whose radii are r1=4cm and r2=5cm.
Now, we draw a chord AC of circle C2, which touches the circle C1 at B.
The tangent at any point of a circle is perpendicular to the radius through the point of contact.
∴ OB is perpendicular to AC.
Now in right-angled triangle, ΔOBC, by using Pythagoras theorem.
OC2=BC2+BO2
[∵ (hypotenuse)2 = (base)2 + ( perpendicular)2]
⇒52=BC2+42⇒BC2=25−16=9⇒BC=3 cm
∴ Length of chord AC = 2BC = 2× 3 = 6 cm
[∵ Line drawn from centre to the chord bisects the chord.]