AD is a tangent of a circle and ABC is the secant. If AB = 8 cm and BC = 10 cm then find the length of AD.

Correct option is D

Given:
AB = 8 cm and BC = 10 cm
Concept Used:
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.
$$AD^2 =$$​ AB (AB + BC)
Solution:

$$AD^2 = AB \times AC \\AD^2 = 8 \times (8+10) \\AD^2 = 144 \\AD = \sqrt{144} = 12 \text{ cm} \\$$​