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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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

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.

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.

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.

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

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” .

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” .