Lesson 11-3 Lesson 11-3 Inscribed AnglesInscribed Angles
An angle is an inscribed angle if its vertex is on a circle and its sides are chords of the circle.
Definitions
B inscribed ais a .n ngle
For the circle above:
AC intercepted arc is the of B.
A
B
C
Theorem 11-9 Inscribed Angle Theorem
1B = AC
2m m
The measure of an inscribed angle is half the measure of its intercepted arc.
A
B
C
Find the values of the variables.Find the values of the variables.
Corollaries to the Inscribed Angle Theorem
1. Two inscribed angles that intercept the same arc are congruent.
A
B
C
D
D B
Corollaries to the Inscribed Angle Theorem
2. An angle inscribed in a semicircle is a right angle.
A
B
C
A
B
C
A
B
C
oIn each case B = . 90,
Corollaries to the Inscribed Angle Theorem
3. The opposite angles of a quadrilateral inscribed in a circle are supplementary.
A
B
C
D
oA + C = 180 . oB + D = 180 .
Find the values of the variables.Find the values of the variables.
Theorem 11-10
1B = ACB
2m m
The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.
A
B
C
B
A
C
Find the values of the variables.Find the values of the variables.
Yes; each is formed by a tangent and a chord, and they intercept the same arc.
45
m A = 100; m B = 75; m C = 80; m D = 105
m X = 80; m Y = 70; m Z = 90; m W = 120
No; the diagonal would be a diameter of O and the inscribed angle would be a right angle, which was not found in Exercise 1 above.
.
GEOMETRY LESSON 11-3GEOMETRY LESSON 11-3
In the diagram below, O circumscribes quadrilateral ABCD and is inscribed in quadrilateral XYZW.
1. Find the measure of each inscribed angle.
2. Find m DCZ.
3. Are XAB and XBA congruent? Explain.
4. Find the angle measures in quadrilateral XYZW.
.
5. Does a diagonal of quadrilateral ABCD intersect the center of the circle? Explain how you can tell.
Homework: Homework:
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