Question 1

We can find the chord length by analyzing the triangle formed by the radii and the chord.

Step 1 — Identify triangle properties

We have a circle. Its center is O. The radius is 12 cm. So, OA and OB are both 12 cm. The central angle AOB is 60°. Consider triangle AOB. Sides OA and OB are equal. This makes triangle AOB isosceles.

Step 2 — Find the base angles

Angles opposite equal sides are equal. So, ∠OAB equals ∠OBA. Let's call them 'x'. The sum of angles in a triangle is 180°. In triangle AOB: $\angle AOB + \angle OAB + \angle OBA = 180^\circ$ $60^\circ + x + x = 180^\circ$ $60^\circ + 2x = 180^\circ$ $2x = 180^\circ - 60^\circ$ $2x = 120^\circ$ $x = \frac{120^\circ}{2}$

$\boxed{x = 60^\circ}$ So, ∠OAB is 60° and ∠OBA is 60°.

Step 3 — Determine the triangle type

All angles in triangle AOB are 60°. ∠AOB is 60°. ∠OAB is 60°. ∠OBA is 60°. This means triangle AOB is equilateral. All sides of an equilateral triangle are equal. So, AB = OA = OB. We know OA is 12 cm. Thus, AB is 12 cm.

Answer

The length of the chord AB is 12 cm.