12.3 Inscribed Angles.

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Presentation transcript:

12.3 Inscribed Angles

12.3 – Inscribed Angles The vertex of C is on O, and the sides of C are chords of the circle. C is an inscribed angle AB is the intercepted arc C B A

12.3 – Inscribed Angles How to find the inscribed angle if you know the arc length m B = mAC 1 2 B C A

12.3 – Inscribed Angles Find a and b P Q R S T 60° 30° b° a°

12.3 – Inscribed Angles 2 inscribed angles that intercept the same arc are congruent. 38° 70° x

12.3 – Inscribed Angles An angle inscribed in a semicircle is a right angle 40° 70° x

12.3 – Inscribed Angles The opposite angles of a quadrilateral inscribed in a circle are supplementary 60° 80° 1 2 3 4

12.3 – Inscribed Angles The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. m C = mBDC 1 2 B C D B C D

12.3 – Inscribed Angles KJ is tangent to circle J. Find x and y K x° 35° y° x°