Homework #8. Suppose that triangle ABC has a 30 degree angle at A and a 60 degree angle at B. Let O be the midpoint of AB. Draw the circle centered at O that goes through A. Explain why this circle also goes through B and C. Angle BOC is called a central angle of the circle because its vertex is at the center. The minor arc BC is called a 60 degree angle because it subtends a 60 degree angle at the center. What is the angular size of minor arc AC? of major arc AC? How does the actual measure of the minor arc AC compare to the measure of minor arc BC?
*Chord ­ a line segment inside the circle whose endpoints are ON the circle
Homework #9. An equilateral triangle is inscribed in the circle of radius 1 centered at the origin (the unit circle). If one of the vertices is (1,0), what are the coordinates of the other two? The three points divide the circle into three arcs. What are the angular sizes of these arcs? Note any special relationships that you see.
120
**an inscribed triangle is a triangle whose vertices are on the circle.
60
12
0
60
60
0
12
** Equal chords cut off equal arcs
#10. On a circle whose center is O, mark points P and A so that minor arc PA is a 46 degree arc. what does this tell you about angle POA? Extend PO to meet the circle again at T. What is the size of the angle PTA? This angle is inscribed in the circle, because all three points are on the circle. The arc PA is intercepted by the angle PTA.
intercepted ­ creates an arc at the points where the angle crosses the circle 46
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