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Rules for Chords, Secants,
and Tangents in Circles
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Theorems:

 

theorem
If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other.
 
rules1
Intersecting Chords Formula:
(segment piece) x (segment piece) =
        (segment piece) x (segment piece)

Formula: a • b = c • d
rules1aa

chordm3
Proof:rule1pg

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theorem
If two secant segments are drawn to a circle from the same external point, the product of the length of one secant segment and its external part is equal to the product of the length of the other secant segment and its external part.
 
rule2
Secant-Secant Formula:
(whole secant) x (external part) =
        (whole secant) x (external part)

Formula: a • b = c • d

rule22pf

rule22pfgiven
Proof:rulessecantpf

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theorem
If a secant segment and tangent segment are drawn to a circle from the same external point, the length of the tangent segment is the geometric mean between the length of the secant segment and the length of the external part of the secant segment.
Alternate   Wording:  
... the product of the length of the secant segment and its external part equals the square of the length of the tangent segment.
 
rule3
Secant-Tangent Formula:
rule3mOR
(whole secant) x (external part) = (tangent)2

Formula: rule3mm
rule3

chordGiven
Proof:
NewProof4

 


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