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Earn +20 ptsQ: What is a two points determine exactly one?
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Can two distinct points both exist on two distinct line?
No. Two points determine one line, and only one.
A tangent line is a line that intersects a circle at exactly two points?
No. A tangent touches the circle at exactly one point. A line that intersects a circle at exactly two points is a secant.
How many different lines are determined by two points?
In classical or Euclidean plane geometry two points defines exactly one line. On a sphere two points can define infinitely many lines only one of which will represent the shortest distance between the points. On other curved surfaces, or in non-Euclidean geometries, the number of lines determined by two points can vary. Even in the Euclidean plane, two points determine infinitely many lines that are not straight!
What is a line that intersects a circle in exactly two points?
secant
What is the unique line postulate?
Unique line assumption. There is exactly one line passing through two distinct points.
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