Geometry and TrigonometryVery hardDistance to the centre along a tangent
Geometry and Trigonometry practice question
A line from a point P touches a circle of radius 6 at point T, so that PT is tangent to the circle. If PT = 8, what is the distance from P to the centre of the circle?
Answer: 10
A tangent is perpendicular to the radius at the point of contact, so the centre, T, and P form a right triangle with legs 6 and 8: the distance is 10.
Common wrong answers
- If you answered 2
- 2 subtracts them.
- If you answered 14
- 14 adds the two lengths.
- If you answered 5.29
- 5.29 is √(64 − 36), treating PT as the hypotenuse.
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