Why the product of secant segments equals the square of a tangent segment
In short: Discover the geometric relationship between a circle, a tangent, and a secant. This proof demonstrates why the product of a secant's external segment and its total length always equals the square of the intersecting tangent segment.
This proof relies on constructing similar triangles to establish a constant ratio between segments. By utilizing the properties of inscribed angles, chords, and tangents, we can confirm this geometric rule holds true for any secant and tangent intersecting at a single point outside a circle.
Understanding this relationship provides a fundamental insight into circle geometry, showing how different lines interacting with a circle's circumference maintain precise, predictable proportions.
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Sources
- Summary by Intellect · source: Proof: The product of segments of intersecting secant and tangent
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