Question

1 AB is tangent to circle O at B. The diagram is not drawn to scale. If AB=12 nd AO=15, what is the length of the radius (r)

Answer 1

r = 9 units

Explanation:

since AB is a tangent to the circle at B , then ∠ ABO = 90°

so Δ ABO is a right triangle

using Pythagoras' identity in the right triangle

OB² + AB² = AO² , that is

r² + 12² = 15²

r² + 144 = 225 ( subtract 144 from both sides )

r² = 81 ( take square root of both sides )

r =
`√(81)` = 9