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Section 10.3 Inscribed Angles

Section 10.3 Inscribed Angles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle

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Page 1: Section 10.3 Inscribed Angles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle

Section 10.3

Inscribed Angles

Page 2: Section 10.3 Inscribed Angles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle

Inscribed Angle

• An angle whose vertex is on a circle and whose sides contain chords of the circle

Inscribed Angle

Page 3: Section 10.3 Inscribed Angles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle

Intercepted Arc

• An arc formed from an inscribed angle on a circle.

Intercepted Arc

Page 4: Section 10.3 Inscribed Angles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle

Measure of an Inscribed Angle

• Half the measure of its intercepted arc

D

A

B

m ADB = ½ m AB

OR

m AB = 2(mADB)50° 100°

Page 5: Section 10.3 Inscribed Angles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle

Examples #1-6

Page 6: Section 10.3 Inscribed Angles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle

Theorem 10.9

• If two inscribed angles of a circle intercept the same arc, then the angles are congruent.

A

CB

DC is congruent to D

It is given that mE 75.

What is the mF?

75

G

E

FH

mF = 75

Page 7: Section 10.3 Inscribed Angles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle

Inscribed

• All of the vertices of a polygon lie on a circle

Page 8: Section 10.3 Inscribed Angles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle

Circumsribed

• Surrounding the figure

Page 9: Section 10.3 Inscribed Angles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle

Theorem 10.10

• If a right triangle is inscribed in a circle, then the hypotenuse is the diameter.

B is a right angle iff

AC is the diameter

A

B C

Page 10: Section 10.3 Inscribed Angles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle

Theorem 10.11

• A quadrilateral can be inscribed in a circle iff its opposite angles are supplementary (180°)

GD

F

E

mD + mF 180

mE + mG 180

Page 11: Section 10.3 Inscribed Angles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle

Examples #1-6

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