http://www.ck12.org Chapter 9. Circles
Concept Problem Revisited
You can take the picture from anywhere on the semicircular walking path. The best place to take the picture is
subjective, but most would think the pale green frame, straight-on, would be the best view.
Vocabulary
Acircleis the set of all points that are the same distance away from a specific point, called thecenter. Aradiusis
the distance from the center to the circle. Achordis a line segment whose endpoints are on a circle. Adiameter
is a chord that passes through the center of the circle. The length of a diameter is two times the length of a radius.
Acentral angleis an angle formed by two radii and whose vertex is at the center of the circle. Aninscribed angle
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 ◦.
Practice
Fill in the blanks.
- An angle inscribed in a ____ is 90◦.
- Two inscribed angles that intercept the same arc are ___.
- The sides of an inscribed angle are ___.
- 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.
5.
6.
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8.
9.Solve forx.
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12.