CK-12 Geometry-Concepts

9.5. Inscribed Angles in Circles http://www.ck12.org

is an angle with its vertex on the circle and whose sides are chords. Theintercepted arcis the arc that is inside the
inscribed angle and whose endpoints are on the angle.

Guided Practice

Findm^6 PMN,mPN̂,m^6 MNP,m^6 LNP, andmLN̂.

Answers:

m^6 PMN=m^6 PLN= 68 ◦by the Congruent Inscribed Angle Theorem.

mPN̂= 2 · 68 ◦= 136 ◦from the Inscribed Angle Theorem.

m^6 MNP= 90 ◦by the Inscribed Angle Semicircle Theorem.

m^6 LNP=^12 · 92 ◦= 46 ◦from the Inscribed Angle Theorem.

To findmLN̂, we need to findm^6 LPN.^6 LPNis the third angle in 4 LPN, so 68◦+ 46 ◦+m^6 LPN= 180 ◦.m^6 LPN=
66 ◦, which means thatmLN̂= 2 · 66 ◦= 132 ◦.

Interactive Practice

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/113000

Explore More

Fill in the blanks.

1. An angle inscribed in a ____ is 90◦.


2. Two inscribed angles that intercept the same arc are ___.


3. The sides of an inscribed angle are ___.


4. Draw inscribed angle^6 JKLin

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M. Then draw central angle^6 JML. How do the two angles relate?

Find the value ofxand/oryin

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A.