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.