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 relate the side lengths of the two given segments (either tangent & secant or secant & secant)

This page:
Two Secants Two Tangents
Tangent and Secant
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
x² = (7+5) • 5
x² = (12) • 5
x² = 60
x =
x² = (7+9) • 7
x² = (16) • 7
x² = 112

This page:
Two Secants Two Tangents
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).
(A +4) • 4 = (5 +8) • 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
(A +8) • 8 = (16 +10) •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
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

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