Circles
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Transcript of Circles
![Page 1: Circles](https://reader036.fdocuments.us/reader036/viewer/2022072016/5681322c550346895d988fa1/html5/thumbnails/1.jpg)
Circles
THEIR
PARTS
AND
![Page 2: Circles](https://reader036.fdocuments.us/reader036/viewer/2022072016/5681322c550346895d988fa1/html5/thumbnails/2.jpg)
Radius
D
I
A
M
E
T
E
R
CHORD
TANGENT
Tangent lines intersecting a diameter or radii at the point of tangency are
perpendicular
A line outside the circle and touching the circle at one
point.
![Page 3: Circles](https://reader036.fdocuments.us/reader036/viewer/2022072016/5681322c550346895d988fa1/html5/thumbnails/3.jpg)
CENTRAL ANGLES
Central Angles- angles whose vertex is at the center of the circle
1200
The intercepted arc of a central angle is equal to
the measure of the central angle
A
B
C
ARC AB = 1200
![Page 4: Circles](https://reader036.fdocuments.us/reader036/viewer/2022072016/5681322c550346895d988fa1/html5/thumbnails/4.jpg)
Inscribed Angle
An inscribed angle is an angle with its vertex ”on” the circle, formed by two
intersecting chords
A
B
CO
Inscribed angle = ½ intercepted Arc
100o
<ABC is an inscribed angle. Its intercepted arc is minor arc from
A to C, therefore
m<ABC = 500
![Page 5: Circles](https://reader036.fdocuments.us/reader036/viewer/2022072016/5681322c550346895d988fa1/html5/thumbnails/5.jpg)
Inscribed Quadrilateral
• A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary
70˚
120˚
40˚
140˚
![Page 6: Circles](https://reader036.fdocuments.us/reader036/viewer/2022072016/5681322c550346895d988fa1/html5/thumbnails/6.jpg)
A Triangle inscribed in a circle
• A triangle inscribed in a semi-circle , having a hypotenuse as a diameter is a right triangle.
30˚
60˚
P
![Page 7: Circles](https://reader036.fdocuments.us/reader036/viewer/2022072016/5681322c550346895d988fa1/html5/thumbnails/7.jpg)
Tangent Chord Angle
B
C
A
120o
An angle formed by an intersecting tangent and chord
with the vertex “on “ the circle.
Tangent Chord Angle = ½ intercepted arc
<ABC is an angle formed by a tangent and chord. Its intercepted arc is the
minor arc from A to B, therefore m<ABC = 60o
![Page 8: Circles](https://reader036.fdocuments.us/reader036/viewer/2022072016/5681322c550346895d988fa1/html5/thumbnails/8.jpg)
Angles formed by intersecting chords (not
diameters)When two chords intersect “inside” a circle, four angles are formed. At the
point of intersection, two sets of vertical angles can be seen in the
corners of the X that is formed on the picture. Remember vertical angles
are equal.
Angle formed inside by two chords=
½ sum of the intercepted arcs
80
5060
170
A B
CD
m< AEB = ½(80 +170) = 1/(250) = 125
E
![Page 9: Circles](https://reader036.fdocuments.us/reader036/viewer/2022072016/5681322c550346895d988fa1/html5/thumbnails/9.jpg)
Angle Formed Outside of a Circle by the Intersection of:
• “Two Tangents”A
B
C
D
2100
150o
The angle is ½ of the difference of the two arcs formed by the
tangents.>ABC = ½(210 – 150) =
30˚
![Page 10: Circles](https://reader036.fdocuments.us/reader036/viewer/2022072016/5681322c550346895d988fa1/html5/thumbnails/10.jpg)
• “Two Secants”
A
B
C
D
E
95o
20o
An angle formed by two secant on the
outside of the circle .The measure of the
angle is ½ the difference of the intersected arcs.
<ACB = ½(95 – 20) = 37.5˚
![Page 11: Circles](https://reader036.fdocuments.us/reader036/viewer/2022072016/5681322c550346895d988fa1/html5/thumbnails/11.jpg)