I'm not able to solve this sum.... please can anyone help me?

Find the length of a chord which is at a disatnt of 8cm from the centre of a circle of radius 10 cm.

Let PQ be a chord of circle with centre O and radius OP and OQ equals to 10 cm.

Draw OA ⊥ PQ

Now OA = 8 cm [ Given, distance of chord from the centre of the circle ]

In right triangle OPA, we have

(OP)² = (OA)² + (PA)²

10² = (8)² + (PA)²

⇒ (PA)² = 100 – 64 = 36

⇒ PA = 6 cm

Now PQ = 2PA [ Since the perpendicular from the centre to a chord bisects the chord ]

∴ PQ = 2 × 6 = 12 cm

Hence, the length of chord is 12 cm.