A tangent at point A of a circle of radius 6 cm meets a line through the centre O at point B. If OB = 10 cm, then the length of AB (in cm) is equal to:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 8.
Given that
A circle of radius (r) = 6 cm
OB = 10 cm
A line PQ through the center O meets at point B
PQ = 2 × 6 = 12 cm,
PB = OP + OB = 6 + 10 = 16 cm,
QB = OB - OQ = 10 - 6 = 4 cm
According to the tangent theorem
AB2 = PB × QB
⇒ AB2 = 16 × 4 = 64
⇒ AB = 8 cm