CHORDS, SECANTS, &
TANGENTS (ANGLE
MEASURES)
9.3.3.8 Know and apply properties of a circle
to solve problems and logically justify results.
Guiding Question: How do I measure
intersecting lines in & out of a circle?
• Lesson Obj: IWBAT
know the properties
of a circle and solve
problems using
them.
• Vocabulary
• Chords
• Secants
• Tangents
• Major/Minor Arc
Guiding
Question: How
do I measure
intersecting lines
in & out of a
circle?
Chords: Any
segment with 2
endpts on the
circle.
Secant: A line
passing through
a circle
Tangent: A line
crossing a circle
at 1 pt. called a
pt. of tangency.
Guiding Question: How do I measure intersecting
lines in & out of a circle?
Recall that a central angle
measure is congruent to its arc.
An inscribed angle is made by 2
chords with a same endpoint.
Guiding Question: How do I measure
intersecting lines in & out of a circle?
• What is the angle
measure of x?
• How big is the
intercepted arc?
Guiding Question: How do I measure intersecting
lines in & out of a circle?
If 2 (or more) inscribed angles
intercept the same arc, they are
congruent!
What if I have intersecting chords?
• How could I find the measure
of angles 1 and 2?
• What kind of angles are
they?
Guiding Question: How do I measure intersecting
lines in & out of a circle?
• 2 chords intersect:
Average the measure
of the intercepted
arcs.
•𝒙=
𝟏𝟕𝟎+𝟕𝟎
𝟐
= 𝟏𝟐𝟎°
Guiding Question: How do I measure intersecting
lines in & out of a circle?
• For any angle
outside the circle(2
secants, 1 secant & 1
tangent): Big arc –
small arc and divide
it by 2.
•𝒙=
𝟖𝟎−𝟐𝟎
𝟐
= 𝟑𝟎°
Guiding Question: How do I measure intersecting
lines in & out of a circle?
For this it will be half of 170
What is the measure of k?
Guiding Question: How do I measure intersecting
lines in & out of a circle?
• Summary:
• Inscribed Angles: Half of central angle intercepting
same arc
• Intersecting chords: Add up the intercepted arcs
and divide by 2
• 2 secants: Big arc – little arc, then divide by 2
• 1 tangent & 1 secant/chord – half of intercepted arc.
Guiding Question: How do I measure intersecting
lines in & out of a circle?
• Assignment: Worksheet