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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Presentation transcript:

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

Measure of an Inscribed Angle Half the measure of its intercepted arc m  ADB = ½ m AB OR m AB = 2(m  ADB) 50° 100°

Examples #1-6

Theorem 10.9 If two inscribed angles of a circle intercept the same arc, then the angles are congruent. A C B D  C is congruent to  D It is given that m  E  75 . What is the m  F? 75  G E F H m  F = 75 

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

Circumsribed Surrounding the figure

Theorem 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

Theorem A quadrilateral can be inscribed in a circle iff its opposite angles are supplementary (180°) m  D + m  F  180  m  E + m  G  180 

Examples #1-6