THEOREMS ON
ANGLES FORMED
BY SECANTS AND
TANGENTS
Presentation by: Lumaniog, Mondragon, and Reyna
POWERPOINT TOPICS
1
RECAP
2
THEOREM
3
ACTIVITY
RECAP!
What are Secants and Tangents?
SECANTS AND TANGENTS
Secants are lines in the same plane as
a circle that intersects two points
Tangent lines are lines in the same plane
as a circle that intersects the circle at
exactly one point
THE TANGENT-SECANT EXTERIOR
ANGLE MEASURE THEOREM
The theorem states that the measure of an angle formed by two
secants, two tangents, or a secant and a tangent drawn from a
point outside a circle is equal to half the difference of the
measures of the intercepted arcs
THE FOLLOWING ARE ALSO TRUE
PROOF
Exterior Angle Theorem:
An exterior angle of a triangle is equal to
the sum of the two opposite interior angle
We can therefore say that:
Finding Angle AEB is =
Since Angle 1 and Angle 2 are =
We arrive to the conclusion of
&
FURTHER PROOF
Therefore
&
are tangent chords
We can then say that
With substitution property, hence
&
WORD PROBLEMS
In circle O shown below, two secants from point P intercept arcs CB
= x – 10 and AD = 2x. What is the measure of arc AD if angle P is
25°?
WORD PROBLEMS
Angles two secants is equal to one half the
difference of the measures of the intercepted arcs
Apply the theorem
Substitute
After substituting, transpose
Multiply both sides by 2:
Simplify
WORD PROBLEMS
Transpose
Since we were given that arc AD = 2x
Angles formed by Secants and Tangents
By Lumaniog, Mondragon, and Reyna
THANK YOU!
Any Questions?
PROOF
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Nunc finibus tincidunt tortor at suscipit. Curabitur justo
metus, pretium nec dui sit amet, tincidunt blandit lacus.
In quis quam elit. Curabitur nec nibh interdum, scelerisque
odio dignissim, sollicitudin turpis. Pellentesque felis odio,
mattis nec nulla vitae.
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Nunc finibus tincidunt tortor at suscipit. Curabitur justo
metus, pretium nec dui sit amet, tincidunt blandit lacus.
In quis quam elit. Curabitur nec nibh interdum, scelerisque
odio dignissim, sollicitudin turpis. Pellentesque felis odio,
mattis nec nulla vitae.
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Nunc finibus tincidunt tortor at suscipit. Curabitur justo
metus, pretium nec dui sit amet, tincidunt blandit lacus.
In quis quam elit. Curabitur nec nibh interdum, scelerisque
odio dignissim, sollicitudin turpis. Pellentesque felis odio,
mattis nec nulla vitae.
TOPIC 3
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Nunc finibus tincidunt tortor at suscipit. Curabitur justo
metus, pretium nec dui sit amet, tincidunt blandit lacus.
In quis quam elit. Curabitur nec nibh interdum, scelerisque
odio dignissim, sollicitudin turpis. Pellentesque felis odio,
mattis nec nulla vitae.
HOMEWORK
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Nunc finibus tincidunt tortor at suscipit. Curabitur justo
metus, pretium nec dui sit amet, tincidunt blandit lacus.
In quis quam elit. Curabitur nec nibh interdum, scelerisque
odio dignissim, sollicitudin turpis. Pellentesque felis odio,
mattis nec nulla vitae.