An angle whose _______________
is ______ the circle and whose
sides contain chords of the circle.
An angle whose _________________ is
the _________________ of the circle
and whose sides are radii of the circle.
Measure of an inscribed Angle
Measure of a central Angle
m ∠ ADB = ½ m AB
m∠APB = m AB
A
P
D
B
B
A
Ex.:
B
A
1. If mBC = 80, then

C
2. If
mBAC = _____°.
mBAC = 35°, then m BC = _____°.
Theorem 10.8: If two inscribed angles of a circle
intercept the same arc, then __________________
_________________________________________
intercepted
arc
Angle A = Angle B
If all the vertices of a polygon lie on a circle,
the polygon is __________________ in the
circle and the circle is _________________
about the polygon.
10.4 Notes: 1
B
Theorem 10.9: If a right triangle is inscribed in a circle, then
_____________________________________
Converse is
also true
A
C
_____________________________________
AC is a diameter, then m∠B = 90o
Theorem 10.10: A quadrilateral can be inscribed in a circle
iff its ____________________________________________
m∠D + m∠F = m∠E + m∠G = 180o
Ex.:
1. Draw a circle with inscribed quadrilateral ABCD.
2. If mA = 50, then mC = _____.
3. If mB = (2x + 5)° and mD = (3x – 10)°,
find x and mB. Show algebra.
4. CHALLENGE! If mB = (x2 + 20)° and mD =
(9x – 2)°, find x and mB. Show algebra.
10.4 Notes: 2
Find the indicated measure(s).
1.) m∠A =_______
2.) m∠A=_______
3.) m∠A=_______
m∠C=_______
4.) m∠C =_______
5.) m BC =_______
7. ) Find the indicated measure in
6.) m∠C =_______
M.
a.) m∠PNO =_______
b.) m∠QNP =_______
c.) m PQ =_______
d.) m QO =_______
e.) m∠NMO =_______
f.) m NOP =_______
g.) m∠QMP =_______
h.) m OQN =_______
8.) Find the value of each variable.
Explain.
A
9.) Find the values of x and y. Then find the
measures of the interior angles of the polygon.
A
B
(17y)°
y°
x°
D
100°
102°
C
(5x)°
(7x)°
B
(19y)°
C
D
x = ______ y = ______
x = _______
y = ______
z = mBCD = ________
m∠DAB = _______ m∠ABC = _______
m∠BCD = _______ m∠CDA = ________
10.4 Notes: 3