Intersecting Secants Theorem

Front

What is the Intersecting Secants Theorem?

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.

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.

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.

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.

Front

What are secants in geometry?

Back

Secants are lines that cut a circle at two points.

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.

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.