In a circle with centre O, ABC is a secant intersecting the circle at A and B and DC is a tangent to the circle at D. If DC = 12 cm and BC = 6 cm, then the length of AB is equal to:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 18 cm.
Given,
DC = 12 cm and BC = 6 cm
We know that,
Tangent secant theorem: The square of the length of the tangent is equal to the product of the length of the secant and its external segment.
In the figure: DC = tangent, BC = secant segment, and AC = external segment
DC2 = BC × (BC + AB)
According to the question;
⇒ 122 = 6 × (6 + AB)
⇒ 144 = 6 × (6 + AB)
⇒ 24 = 6 + AB
⇒ AB = 18 cm