The radii of two concentric circles are 35 cm and 21 cm. If the chord of the greater circle is a tangent to the smaller circle, then the length of that chord is:

Correct option is C

Given:

A chord MN as shown is tangent to smaller circle of radius 21cm
Radius ON is 35 cm
P is mid point of MN
Formula Used:
Tangent is always perpendicular from centre. Hence OP⊥ MN
Pythagoras’ theorem
Solution:
We know that ∆OPN is right angled triangle. Hence
ON = 35 cm, OP = 21cm
​$$(ON)^2 = (OP)^2 + (PN)^2 \\(35)^2 = (21)^2 + (PN)^2 \\(PN)^2 = (35)^2 - (21)^2 \\(PN)^2 = 784 \\PN = 28 \, \text{cm}$$​​
Length of chord = 2$$\times$$​PN = 56cm