

Side Length of Tangent & Secant of a CircleTangents, 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)
This page:Two Secants Two Tangents Related Pages: Circles forumula, graph, equations  Equation of A Circle  Circumference  Area  Chord  Tangent Arc of A Circle  Intersecting Chords Inscribed Angle Secant of circle  2 Tangents from 1 point Central Angle  Angles, Arc, Secants, tangents Tangents, Secants and Side Lengths  Tangent and a Chord  images Free Math Printable Worksheets: Circles Worksheets and Activites for Math Teachers 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.
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.
In the diagram on the left, the red line is a tangent, how long is it?
x² = (7+5) • 5 x² = (12) • 5 x² = 60 x =
In the problem below, the red line is a tangent of the circle, what is its length?
x² = (7+9) • 7 x² = (16) • 7 x² = 112 x = Two Secants IntersectingIf 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).
Use the theorem above to determine A if B= 4, C=8, and D=5
(A +4) • 4 = (13) • 5 (A +4) • 4 = 65 (A +4) = 65 ÷4 (A +4) = 16.25 A = 16.25 − 4 A = 12.25 Use the theorem above to determine A if B= 8, C=16, and D = 10
(A +8) • 8 = (26) • 10 (A +8) • 8 = 260 (A +8) = 2,60÷ 8 (A +8) = 32.5 A = 32.5 − 8 A = 24.5 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?
How to use the theorem to find side LM KO • JO = LO • MO JO = KO − KJ JO = 16 − 4 = 12 KO • JO = LO • MO 16 • 12 = 32 • MO 192= 32 • MO 192/32= MO 6 = MO LM = LO − MO LM = 32 − 6 =26 