Download Find the measure of each arc of circle P, where RT is a diameter

Geometry
Notes
Name_________________________
Finding Arc Measures & Inscribed Angles
central angle –
A
minor arc –
C
major arc –
D
B
semicircle –
Measuring Arcs
The measure of an arc is EQUAL to the measure of its corresponding central angle
Examples 1 – 3: Find the measure of each arc of circle P, where RT is a diameter.
1. RS
R
P
3. RTS
4. RST
110
T
S
Properties of Arcs
An arc formed by two adjacent arcs is the sum of the measure of the two arcs.
Two arcs are congruent iff their corresponding chords are congruent.
Examples 4 – 9: Identify the given arc as a minor arc, major arc, or semicircle. Then
find the measure of each arc.
4. TQ
5. QRT
6. TQR
T
80
7. QS
inscribed angle –
intercepted arc –
8. TS
9. RST
S
120
60
Q
R
Properties of Inscribed Angles and Intercepted Arcs
The measure of an inscribed angle is one half the measure of its intercepted arc.
If two inscribed angles intercept the same arc, then the angles are congruent.
Examples 10 – 11: Find the indicated measure in circle P. Q
10. mT
11. QR
P
50
R
48
Example 12
Find the measure of RS and mSTR.
R
T
T
S
S
31
U
Examples 13 – 15: Find the measure indicated.
13. FGH
14. TV
H
T
U
38
D
G
15. WXZ
Y
X
72
90
F
Z
V
W
A polygon is an inscribed polygon if all of its vertices lie on the circle. The circle that contains the
vertices is a circumscribed circle.
Properties of Inscribed Polygons
If a right triangle is inscribed in a circle, then the hypotenuse is the diameter.
A quadrilateral can be inscribed in a circle iff its opposite angles are supplementary.
Examples 16 – 17: Find the value of each variable.
16.
17.