Question

What is the length of BD

Answer 1

BD = 3 units

Explanation:

since AB is a tangent to the circle, then the angle between the tangent and the radius at the point of contact A is 90°

Then Δ ABC is right

using Pythagoras' identity in the right triangle

BC² = AC² + AB² = 4.5² + 6² = 20.25 + 36 = 56.25 ( take square root of both sides )

BC =
`√(56.25)` = 7.5

now CD is a radius of the circle = 4.5

Then

BD = BC - CD = 7.5 - 4.5 = 3 units