Download 10.3 Guided Notes

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10.3 Notes ~ Inscribed Angles
Date: ____________________________
Geometry Advanced
Objective:
1) Find the measure of inscribed angles and their intercepted arcs.
 An INSCRIBED ANGLE is an angle whose vertex is on a circle and whose sides contain chords of the
circle.
 The arc that lies in the interior of an inscribed angle and has endpoints on the angle is called the
INTERCEPTED ARC.
Measure of an Inscribed Angle
If an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc.
mADC 

1
m AB
2
or

2mADC   m AB
1
Measure of the Intercepted Arc
2
2(Measure of the Inscribed Angle) = Measure of the Intercepted Arc
Measure of Inscribed Angle =
If two inscribed angles in a circle intercept the same arc, then the angles are congruent.

ACB and ADB both intercept AB therefore ACB  ADB
Example 1
Find the values of x
A.
D.
B.
C.
E.
 If all the vertices of a polygon lie on a circle, then the polygon is INSCRIBED in the circle and the circle
is CIRCUMSCRIBED about the polygon.
If a right triangle is inscribed in a circle,
then the hypotenuse is a diameter of the circle.
If one side of an inscribed triangle is a diameter of the circle,
then the triangle is a right triangle and the angle opposite the diameter is the right angle.
A quadrilateral can be inscribed in a circle
if and only if its opposite angles are supplementary.
If quadrilateral DEFG is inscribed in circle C then  E and  G are supplementary and  D and  F
are supplementary. (Note: The converse is also true because it is a biconditional)
Example 2
A. AB is a diameter

B. Quadrilateral WXYZ is inscribed in circle P.
Practice Problems
In P, RS || TV , m SV = 86o, and m  RPS = 110o. Find each measure.

1. m RS
2. m  SRV
3. m  STV
4. m  SVR
5. m  RTV
6. m  RTS
7. m  PRS
8. m  RSP
9. m  RVT
10. m  SVT
11. m  TQV
12. m  RQT
13. m  QRT
14. m TV
15. m  SRT
16. m  TSV
17. m RT


18. m  RST