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Side Length of Tangent & Secant of a Circle

Tangents, secants, Side Lengths Theorems & Formula

If a tangent and a secant or if two secants intersect from a point outside of the circle, then there are two useful theorems/formula that allow relate the side lengths of the two given segments (either tangent & secant or secant & secant)

Tangent and Secants

If a secant and a tangent of a circle are drawn from a point outside the circle, then the product of the lengths of the secant and its external segment equals the square of the length of the tangent segment.
Picture of tangent secant and sides
Practice Problems


Lengths of secant and a tangent
Use the theorem for the intersection of a tangent and a secant of a circle to solve the problems below. picture of intersection of  secant and a tangent
In the diagram on the left, the red line is a tangent, how long is it?
Length of Tangent

In the problem below, the red line is a tangent of the circle, what is its length?
Length of tangent

Two Secants Intersecting
If two secant segments are drawn from a point outisde a circle, the product of the lengths(C+D) of one secant segment and its exteranal segment(D) equals the product of the lengths (A+B) of the other secant segment and its external segment(B).
Product of segments of secants from point out of circle
Use the theorem above to determine A if B= 4, C=8, and D=5
Answer
Use the theorem above to determine A if B= 8, C=16, and D = 10
practice finding secant length
Answer
The two secants in the picture below are not drawn to scale. If KO = 16, KJ =4, and LO = 32, what is the measure of LM?
Answer

practice problem two secants side length formula