Geometry Intermediate

Chord, Secant & Tangent Relationships

Apply the power-of-a-point theorem for intersecting chords, a tangent and secant, or two secants from an external point. Give three known lengths and find the fourth.

3 theorem types
Solve for any unknown
Labeled diagram
Input
Try:

t = tangent length; p = external secant segment; q = whole secant length (p + chord inside).

Try:

p₁, p₂ = external segments; q₁, q₂ = whole secant lengths from external point.

Try:
Result
Select theorem and enter known values.
Step-by-Step Solution
Diagram
Power of a Point
Intersecting chords: AE·EB = CE·ED Tangent-secant: t² = p·q Two secants: p₁·q₁ = p₂·q₂
Why it works

All three cases are versions of the Power of a Point theorem. The product of signed distances from a fixed point to any two intersection points with a circle is constant — regardless of which line you draw through that point.

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