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

Given:

AB = 4 cm and BC = 5 cm

Concept:

Tangent secant segment theorem: If a tangent and secant meet at a common point outside a circle, the segments created have a similar relationship to that of two secant rays.

⇒ AD² = AB (AB + BC)      

Calculation:

Using tangent secant segment theorem, we have,

AD2 = AB (AB + BC)     

⇒ AD2 = 4 (4 + 5)

⇒ AD2 = 36

⇒ AD = 6 cm