﻿ Tangent, secants, and their side lengths from a point outside the circle. Theorems and formula to calculate length of tangent & Secant

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

Tangent and Secant
Two Secants

### 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

x² = (7+5) • 5
x² = (12) • 5
x² = 60
x =

x² = (7+9) • 7
x² = (16) • 7
x² = 112

#### 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

KOJO = LO MO
JO = KOKJ
JO = 16 − 4 = 12
KOJO = LO MO
16 • 12 = 32 • MO
192= 32 • MO
192/32= MO
6 = MO
LM = LOMO
LM = 32 − 6 =26

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