In the given figure, OM = ON. If CN = (2x − 1) cm and AB = 16 cm, then what is the value of x?

It is known that chords of a circle which are equidistant from the centre are equal.

Now, OM⊥AB and ON⊥CD, and OM = ON

∴ AB = CD

⇒ CD = 16 cm

The perpendicular from the centre of a circle to the chord bisects the chord.

∴ CN = ND

⇒ CD = 2 × CN = 2 (2x − 1) cm

⇒ 2 (2x − 1) cm = 16 cm

⇒ (2x − 1) cm = 8 cm

⇒ 2x = 9 cm

$\Rightarrow x=\frac{9}{2}=4.5 cm$

Thus, the value of x is 4.5 cm.