In the diagram , AD is the tangent line of the circle and ABC is the secant line. If AB = 4 cm and BC = 5 cm, then the length of AD is

​

Correct option is C

Given:

AB = 4 cm

BC = 5 cm

AD is the tangent to the circle from point A

ABC is a secant line intersecting the circle at points B and C

Concept Used:
Tangent-Secant Theorem — If a tangent and a secant are drawn from an external point to a circle, then:
(Tangent length)² = (External part of secant) × (Total length of secant)

Formula Used:
AD² = AB × AC

Solution:

AC = AB + BC = 4 + 5 = 9 cm

AD² = 4 × 9 = 36

AD = √36 = 6 cm