In a circle centered at O, PQ is a tangent at P. Furthermore, AB is the chord of the circle and is extended to Q. If PQ = 12 cm and QB = 8 cm, then the length of AB is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 10 cm.
Given that
In a circle centered at O, PQ is a tangent at P
If PQ = 12 cm and QB = 8 cm
According to the circle tangent theorem
⇒ PQ2 = AQ × BQ
⇒ 122 = (AB + 8) × 8
⇒ AB + 8 = 144/8 = 18
⇒ AB = 18 - 8 = 10 cm