Geometry and TrigonometryMediumTangent meets radius at a right angle
Geometry and Trigonometry practice question
A line is tangent to a circle of radius 5 at point T. Point P lies on the tangent line, 12 units from T. What is the distance from P to the centre of the circle?
Answer: 13
A radius drawn to the point of tangency is perpendicular to the tangent, so the centre O, the point T and the point P form a right triangle with legs OT = 5 and TP = 12. The hypotenuse OP = √(25 + 144) = √169 = 13.
Common wrong answers
- If you answered 7
- 7 is 12 − 5. The centre is not on the tangent line; OP is the hypotenuse of a right triangle.
- If you answered 17
- 17 is 5 + 12. The distances form a right triangle, so use the Pythagorean theorem, not addition.
- If you answered 119
- 119 is 144 − 25, subtracting the squares as if 12 were the hypotenuse. The distance from P to the centre is the longest side, so ADD: 25 + 144 = 169.
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