1. Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle. A A C C A B B C B
All three of these inscribed angles intercept arc AB.

2. Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle. A A C C A B B C B
All three of these inscribed angles intercept arc AB.
Theorem : An inscribed angle is equal to half of its intercepted arc.

3. Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle. A A C
32° 1 C
200° 2 A B
40° 3 B C B
Theorem : An inscribed angle is equal to half of its intercepted arc.
EXAMPLE : Find the measure of angles 1 , 2 and 3.

4. Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle. A A C
32° 1 C
200° 2 A B
40° 3 B C B
Theorem : An inscribed angle is equal to half of its intercepted arc.
EXAMPLE : Find the measure of angles 1 , 2 and 3.

5. Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle. A A C
32° 1 C
200° 2 A B
40° 3 B C B
Theorem : An inscribed angle is equal to half of its intercepted arc.
EXAMPLE : Find the measure of angles 1 , 2 and 3.

6. Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle. A A C
32° 1 C
200° 2 A B
40° 3 B C B
Theorem : An inscribed angle is equal to half of its intercepted arc.
EXAMPLE : Find the measure of angles 1 , 2 and 3.

7. Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle. A A C ?
86° C ? A
25° B ?
18° B C B
Theorem : An inscribed angle is equal to half of its intercepted arc.
EXAMPLE #2 : Find the measure of arc AB in each example.

8. Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle. A A C ?
86° C ? A
25° B ?
18° B C B
Theorem : An inscribed angle is equal to half of its intercepted arc.
EXAMPLE #2 : Find the measure of arc AB in each example.
Take notice that the arc is two time bigger than the angle.

9. Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle. A A C ?
86° C ? A
25° B ?
18° B C B
Theorem : An inscribed angle is equal to half of its intercepted arc.
EXAMPLE #2 : Find the measure of arc AB in each example.
Take notice that the arc is two times bigger than the angle.

10. Geometry – Inscribed and Other Angles
Inscribed Angle – an angle whose vertex lies on the circle and its sides are chords of the circle. A A C
36°
86° C ? A
25° B
50°
18° B C B
Theorem : An inscribed angle is equal to half of its intercepted arc.
EXAMPLE #2 : Find the measure of arc AB in each example.
Take notice that the arc is two times bigger than the angle.

11. Geometry – Inscribed and Other Angles
Theorem : An angle formed by a tangent line and a chord is equal to half of its intercepted arc. A 1 B

12. Geometry – Inscribed and Other Angles
Theorem : An angle formed by a tangent line and a chord is equal to half of its intercepted arc. A 1 B
EXAMPLE : If arc AB = 65°, find the measure of angle 1.

13. Geometry – Inscribed and Other Angles
Theorem : An angle formed by a tangent line and a chord is equal to half of its intercepted arc. A 1 B
EXAMPLE : If arc AB = 65°, find the measure of angle 1.

14. Geometry – Inscribed and Other Angles
Theorem : An angle formed by a tangent line and a chord is equal to half of its intercepted arc. X A 1 B
EXAMPLE #2 : If arc AXB = 300°, find the measure of angle 1.

15. Geometry – Inscribed and Other Angles
Theorem : An angle formed by a tangent line and a chord is equal to half of its intercepted arc. X A 1 B
EXAMPLE #2 : If arc AXB = 300°, find the measure of angle 1.

16. Geometry – Inscribed and Other Angles
Theorem : An angle formed by two chords is equal to half of the sum of the intercepted arcs C A X B D

17. Geometry – Inscribed and Other Angles
Theorem : An angle formed by two chords is equal to half of the sum of the intercepted arcs C
40° A X B D
42°
EXAMPLE : Arc AC = 40° and arc BD = 42°.
Find the measure of angle CXA.

18. Geometry – Inscribed and Other Angles
Theorem : An angle formed by two chords is equal to half of the sum of the intercepted arcs C ? A X B D
50°
EXAMPLE # 2 : Angle CXA = 40° and arc BD = 50°.
Find the measure of arc CA.

19. Geometry – Inscribed and Other Angles
Theorem : An angle formed by two chords is equal to half of the sum of the intercepted arcs C y A X B D
50°
EXAMPLE # 2 : Angle CXA = 40° and arc BD = 50°.
Find the measure of arc CA.

20. Geometry – Inscribed and Other Angles
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 ) D C X A B

21. Geometry – Inscribed and Other Angles
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 ) D C
75°
23° X A B
EXAMPLE : Arc BD = 75° and arc CA = 23°. Find the measure of angle “x” .

22. Geometry – Inscribed and Other Angles
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 ) D C
75°
23° X A B
EXAMPLE : Arc BD = 75° and arc CA = 23°. Find the measure of angle “x” .