Two circles of radii 12 cm and 13 cm are concentric. The length of the chord of the larger circle that touches the smaller circle is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 10 cm.
Given that
Two circles of radii 12 cm and 13 cm are concentric
The chord PQ touches the small circle at S
OP = 13 cm, OS = 12 cm
In triangle OPS,
⇒ OP2 = OS2 + PS2
⇒ PS2 = 132 - 122 = 169 - 144 = 25
⇒ PS = 5 cm
Hence, the chord length PQ = 2 × 5 = 10 cm