問題一覧
1
an angle whose vertex is on a circle and whose sides contain chords of the circle
inscribed angle
2
an arc that lies in the interior of an inscribed angle and has endpoints on the angle
intercepted arc
3
if an angle is inscribed in a circle then the measure of the angle equals 1/2 the measure of its intercepted arc
theorem 4a
4
the measure of the intercepted arc is twice the measure of the inscribed angle
theorem 4b
5
if two inscribed angles of a circle (or congruent circles) intercept congruent arcs or the same arc, then the angles are congruent
theorem 5
6
if an inscribed angle of a circle intercepts a semicircle, then the angle is a right angle
theorem 6
7
if a quadrilateral is inscribed in a circle, then its opposite angles are supplementary
theorem 7
8
a line coplanar with the circle and intersects it at one and only one point
tangent to a circle
9
the point of intersection of the tangent line and the circle
point of tangency
10
at a given point on a circle, one and only one line can be drawn that is tangent to the circle
postulate 2
11
if a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency
theorem 8
12
if a line is perpendicular to a radius of a circle at its endpoint that is on the circle, then the line is tangent to the circle
theorem 9
13
if two segments from the same exterior point are tangent to a circle then the two segment are congruent
theorem 10
14
a line that is tangent to two circles on the same plane
common tangent
15
tangents that intersect the segment joining the center of the two circles
common internal tangents
16
tangents which do not intersect the segment joining the centers of the two circles
common external tangents
17
a line that intersects a circle at exactly two points. a secant contains a chord of a circle
secant
18
if two secants intersect in the exterior of a circle, then the measure of the angle formed is 1/2 the positive difference of the measures of the intercepted arcs
theorem 11
19
if a secant and a tangent intersect in the exterior of a circle, then the measure of the angle formed is 1/2 the positive difference of the measures of the intercepted arcs
theorem 12
20
if two tangents intersect in the exterior of a circle, then the measure of the angle form is 1/2 the positive difference of the measures of the intercepted arcs
theorem 13
21
if two secants intersect in the interior of a circle, then the measure of an angle formed is 1/2 the sum of the measures of the arcs intercepted by the angle and its vertical angle
theorem 14
22
if a secant and a tangent intersect at the point of tangency, then the measure of each angle form is 1/2 the measures of its intercepted arc
theorem 15
23
the part of a secant segment that is outside the circle
external secant segment
24
if two chords of a circle intersect, then the product of the measures of the segments of one chord is equal to the product of the measures of the segments of the other chord
theorem 16
25
if two second segments are drawn to a circle from an exterior point, then the product of the lengths of 1 second segment and its external secant segment is equal to the product of the lengths of the other second segment and its external secant segment
theorem 17
26
if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the length of the tangent segment is equal to the product of the length of the secant segment and its external secant segment
theorem 18