Geometry and TrigonometryVery hardLength of a tangent from an external point
Geometry and Trigonometry practice question
A circle has centre O and radius 9. A point P lies 15 units from O, and a line from P touches the circle at a single point T. What is the length of PT?
Answer: 12
The radius OT is perpendicular to the tangent, so PT = √(15² − 9²) = 12.
Common wrong answers
- If you answered 6
- 6 subtracts 9 from 15.
- If you answered 24
- 24 adds them.
- If you answered 17.5
- 17.5 adds the squares.
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