A chord of length 12 units in a circle of radius 10 units is ______ units away from its centre.

Correct option is A

Given:

A chord MN as shown is 12 units
Radius ON is 10 units
P is mid point of MN
Formula Used:
Perpendicular from mid point of chord passes through centre. Hence OP⊥ MN
Pythagoras’ theorem
Solution:
We know that ∆OPN is right angled triangle. Hence
ON = 10 units, PN = $$\frac{MN}{2}$$​ = 6 units
​$$(ON)^2 = (OP)^2 + (PN)^2\\(10)^2 = (OP)^2 + (6)^2\\(OP)^2 = (100)^2 - (36)^2\\(OP)^2= 64\\OP= 8 units\\$$​​