Geometry and TrigonometryMediumDistance from an external point to a circle's centre via a tangent
Geometry and Trigonometry practice question
A line through point P is tangent to a circle of radius 5 at point T, and PT = 12. What is the distance from P to the centre of the circle?
Answer: 13
A radius meets a tangent at a right angle, so the centre O, T, and P form a right triangle with legs OT = 5 and PT = 12: OP = √(25 + 144) = 13.
Common wrong answers
- If you answered 7
- 7 is 12 − 5.
- If you answered 17
- 17 is 5 + 12, adding the legs instead of using the Pythagorean theorem.
- If you answered 10.9
- 10.9 is √(144 − 25), treating PT as the hypotenuse.
More Geometry and Trigonometry questions
- Medium
In a 45°-45°-90° right triangle, each leg has length 5. What is the length of the hypotenuse? - Medium
A cylinder has a radius of 3 and a height of 10. What is its volume? (Use V = πr²h.) - Medium
In a right triangle, the side opposite angle θ has length 3 and the hypotenuse has length 5. What is sin θ? - Medium
Two triangles are similar with a ratio of 2 to 3. A side of the smaller triangle measures 8. What is the lengt… - Medium
What is the distance between the points (1, 2) and (4, 6) in the coordinate plane? - Medium
A circle has a radius of 6. What is the area of a sector with a central angle of 60°?
Not affiliated with the College Board. SAT is a trademark of the College Board.