What is the Intersecting Secants Theorem?

Intersecting Secants Theorem

Flashcard
•
Mathematics
•
11th Grade
•
Hard
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7 questions
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1.
FLASHCARD QUESTION
Front
Back
It states that if two secants intersect outside a circle, the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment.
2.
FLASHCARD QUESTION
Front
What happens when both lines are tangents in the Intersecting Secants Theorem?
Back
When both lines are tangents, the theorem simplifies to c² = a × b, where c is the length of the tangent.
3.
FLASHCARD QUESTION
Front
What is the relationship between the lengths a, b, c, and d in the theorem?
Back
The relationship is given by the equation a/d = c/b, which leads to a × b = c × d.
4.
FLASHCARD QUESTION
Front
Why does the Intersecting Secants Theorem hold true?
Back
It holds true because the triangles formed by the secants and the circle are similar triangles, sharing angles θ and φ.
5.
FLASHCARD QUESTION
Front
What are secants in geometry?
Back
Secants are lines that cut a circle at two points.
6.
FLASHCARD QUESTION
Front
What is the significance of measuring lengths accurately in the theorem?
Back
Accurate measurements ensure that the products of the lengths are equal, confirming the theorem's validity.
7.
FLASHCARD QUESTION
Front
What can you do to understand the Intersecting Secants Theorem better?
Back
You can draw a diagram, measure the lengths of the secants, and verify the theorem by calculating the products.
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