Geometry and TrigonometryMediumHalf-chord from a circle's equation
Geometry and Trigonometry practice question
In the xy-plane, a circle has the equation x² + y² = 25. The horizontal line y = −3 meets the circle at two points. What is the distance between those two points?
Answer: 8
At y = −3, x² = 25 − 9 = 16, so x = ±4 and the points are 8 apart.
Common wrong answers
- If you answered 4
- 4 is the distance from the y-axis to one of the points.
- If you answered 10
- 10 is the diameter; the chord at y = −3 is shorter.
- If you answered 16
- 16 is x², not the distance.
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.