Term
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Definition
| an angle formed by any two radii of a circle. formally in our geometry, an angle is a central angle of a circle if and only if the vertex of the angle is the center of the circle and the sides are radii of the circle |
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Term
| inscribed angle of a circle |
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Definition
| an angle formed by any two chords with a common endpoint. formally in our geometry, an angle is an inscribed angle of a circle if and only if the vertex of the angle is on the circle, and the sides are chords of the circle |
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Term
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Definition
| an angle intercepts an arc if and only if each of the following conditions hold. 1) the endpoints of the arc lie on the sides of the angles. 2) each side of the angle contains one endpoint of the arc. 3) all points on the arc except the endpoints lie in the interior of the angle |
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Term
| measure of a central angle of a circle |
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Definition
| based on relationship with the points on a circle this is defined as the measure of the angle's intercepted arc of the circle |
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Term
| measure of the arc of a circle |
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Definition
| based on its relationship with the central angles of a circle, this is defined as the measure of the central angle which interperets the arc |
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Term
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Definition
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Term
postulate 8, circle
assumption 1 |
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Definition
| the set of all points on a circle can be put into a one to one correspondence with the real numbers from 0 to 360 inclusive with the exception of any one point which may be paired with 0 and 360 |
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Term
postulate 8, circle
assumption 2 |
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Definition
| to every pair of points on a circle there correspond exactly 2 real numbers whose sum is 360 each of which may be called the distance between the 2 points |
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Term
postulate 8, circle
assumption 3 |
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Definition
| the distance between any 2 points on a circle is the absolute value of the difference between their coordinates |
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Term
postulate 8, circle
assumption 4 (arc addition assumption) |
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Definition
| if on a circle, a point B lies between points A and C then mAB + mBC = mAC |
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