geometry – inscribed and other angles inscribed angle – an angle whose vertex lies on the circle...
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Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle.
C
B
A
CA
B C
A
B
All three of these inscribed angles intercept arc AB.
Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle.
C
B
A
CA
B C
A
B
All three of these inscribed angles intercept arc AB.
Theorem : An inscribed angle is equal to half of its intercepted arc.
AB2
1C
Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle.
C
B
A
CA
B C
A
B
Theorem : An inscribed angle is equal to half of its intercepted arc. AB2
1C
EXAMPLE : Find the measure of angles 1 , 2 and 3.
200°1
2
340°
32°
Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle.
C
B
A
CA
B C
A
B
Theorem : An inscribed angle is equal to half of its intercepted arc. AB2
1C
EXAMPLE : Find the measure of angles 1 , 2 and 3.
200°1
2
340°
32°
10012
2001
Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle.
C
B
A
CA
B C
A
B
Theorem : An inscribed angle is equal to half of its intercepted arc. AB2
1C
EXAMPLE : Find the measure of angles 1 , 2 and 3.
200°1
2
340°
32°
10012
2001
2022
402
Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle.
C
B
A
CA
B C
A
B
Theorem : An inscribed angle is equal to half of its intercepted arc. AB2
1C
EXAMPLE : Find the measure of angles 1 , 2 and 3.
200°1
2
340°
32°
10012
2001
2022
402
1632
323
Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle.
C
B
A
CA
B C
A
B
Theorem : An inscribed angle is equal to half of its intercepted arc. AB2
1C
EXAMPLE #2 : Find the measure of arc AB in each example.
?86°
25°18°?
?
Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle.
C
B
A
CA
B C
A
B
Theorem : An inscribed angle is equal to half of its intercepted arc. AB2
1C
EXAMPLE #2 : Find the measure of arc AB in each example.
?86°
25°18°?
?
AB172
AB22
1286
AB2
186
Take notice that the arc is two time bigger than the angle.
Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle.
C
B
A
CA
B C
A
B
Theorem : An inscribed angle is equal to half of its intercepted arc. AB2
1C
EXAMPLE #2 : Find the measure of arc AB in each example.
?86°
25°18°?
?
AB172
AB22
1286
AB2
186
Take notice that the arc is two times bigger than the angle.
AB2 C
Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle.
C
B
A
CA
B C
A
B
Theorem : An inscribed angle is equal to half of its intercepted arc. AB2
1C
EXAMPLE #2 : Find the measure of arc AB in each example.
?86°
25°18°50°
36°
AB172
AB22
1286
AB2
186
Take notice that the arc is two times bigger than the angle.
AB2 C
36182
50252
Geometry – Inscribed and Other Angles
B
A
Theorem : An angle formed by a tangent line and a chord is equal to half of its intercepted arc.
AB2
11
1
Geometry – Inscribed and Other Angles
B
A
Theorem : An angle formed by a tangent line and a chord is equal to half of its intercepted arc.
AB2
11
1
EXAMPLE : If arc AB = 65°, find the measure of angle 1.
Geometry – Inscribed and Other Angles
B
A
Theorem : An angle formed by a tangent line and a chord is equal to half of its intercepted arc.
AB2
11
1
EXAMPLE : If arc AB = 65°, find the measure of angle 1.
5.321
652
11
Geometry – Inscribed and Other Angles
B
A
Theorem : An angle formed by a tangent line and a chord is equal to half of its intercepted arc.
AB2
11
1
EXAMPLE #2 : If arc AXB = 300°, find the measure of angle 1.
X
60AB
300360AB
AXB 360AB
Geometry – Inscribed and Other Angles
B
A
Theorem : An angle formed by a tangent line and a chord is equal to half of its intercepted arc.
AB2
11
1
EXAMPLE #2 : If arc AXB = 300°, find the measure of angle 1.
X
60AB
300360AB
AXB 360AB
301
602
11
Geometry – Inscribed and Other Angles
B
A
Theorem : An angle formed by two chords is equal to half of the sum of the intercepted arcs
BD AC2
1CXA
D
C
X
Geometry – Inscribed and Other Angles
B
A
Theorem : An angle formed by two chords is equal to half of the sum of the intercepted arcs
BD AC2
1CXA
D
C
X
EXAMPLE : Arc AC = 40° and arc BD = 42°.
Find the measure of angle CXA.
40°
42°
41CXA
822
1CXA
42402
1CXA
Geometry – Inscribed and Other Angles
B
A
Theorem : An angle formed by two chords is equal to half of the sum of the intercepted arcs
BD AC2
1CXA
D
C
X
EXAMPLE # 2 : Angle CXA = 40° and arc BD = 50°.
Find the measure of arc CA.
?
50°
Geometry – Inscribed and Other Angles
B
A
Theorem : An angle formed by two chords is equal to half of the sum of the intercepted arcs
BD AC2
1CXA
D
C
X
EXAMPLE # 2 : Angle CXA = 40° and arc BD = 50°.
Find the measure of arc CA.
y
50°
y
y
y
y
30
5080
2502
1240
502
140
Geometry – Inscribed and Other Angles
B
A
Theorem : An angle formed by two secants is equal to half of the difference of the intercepted arcs. ( a secant is a line that cuts through a circle )
AC BD2
1X
D
C
X
Geometry – Inscribed and Other Angles
B
A
Theorem : An angle formed by two secants is equal to half of the difference of the intercepted arcs. ( a secant is a line that cuts through a circle )
AC BD2
1X
D
C
X
EXAMPLE : Arc BD = 75° and arc CA = 23°. Find the measure of angle “x” .
75°
23°
Geometry – Inscribed and Other Angles
B
A
Theorem : An angle formed by two secants is equal to half of the difference of the intercepted arcs. ( a secant is a line that cuts through a circle )
AC BD2
1X
D
C
X
EXAMPLE : Arc BD = 75° and arc CA = 23°. Find the measure of angle “x” .
75°
23°
26X
522
1X
23752
1X