42 terms

# Honors Geometry Exam Review - Chapter 10

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Circle
The set of all point in a plane that are equidistant from a given point called the center of the circle. (Page- 651)
Center of a Circle
The exact middle of a circle. (Page- 651)
A segment whose endpoints are the center and any point on the circle. (Page- 651)
Chord
A segment whose endpoints are on a circle. (Page- 651)
Diameter
A chord that contains the center of the circle. (Page- 651)
Secant
A line that intersects a circle in 2 points. (Page- 651)
Tangent
A line in the plane of a circle that intersects the circles in exactly 1 point, the point of tangency. (Page- 651)
Theorem 10.1
In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle. (Page- 653)
Theorem 10.2
Tangent segments from a common external point are congruent. (Page- 654)
Central Angle
An angle whose vertex is the center of the circle. (Page- 659)
Minor Arc
Part of a circle that measures less then 180°. (Page- 659)
Major Arc
Part of a circle that measures between 180° and 360°. (Page- 659)
Semicircle
An arc with endpoints that are the endpoints of a diameter. (Its 180°). (Page- 659)
Measure of a Minor Arc
The measure of its central angle. (Page- 659)
Measure of a Major Arc
The difference between 360° and the measure of the related minor arc.
The measure of an arc formed by 2 adjacent arcs is the sum of the measures of the 2 arcs. (Page- 660)
Congruent Circles
2 circles are congruent if they have the same radius. (Page- 660)
Congruent Arcs
2 arcs are congruent if they have the same measure and they are arcs of the same circle or of congruent circles. (Page- 660)
Theorem 10.3
In the same circle, or in congruent circles, 2 minor arcs are congruent if and only it their corresponding chords are congruent. (Page- 664)
Theorem 10.4
If one chord is a perpendicular bisector of another chord, the first chord is a diameter. (Page- 665)
Theorem 10.5
If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. (Page- 665)
Theorem 10.6
In then same circle, or in congruent circles, 2 chords are congruent if and only if they are equidistant from the center. (Page- 666)
Inscribed Angle
An angle whose vertex is on a circle and whose sides contain chords of the circle. (Page- 672)
Intercepted Arc
The arc that lies in the interior of an inscribed angle and has endpoints of the angle. (Page- 672)
Measure of an Inscribed Angle Theorem
The measure of an inscribed angle is ½ the measure of its intercepted arc. (Page- 672)
Theorem 10.8
If 2 inscribed angles of a circle intercept the same arc, then the angles are congruent. (Page- 673)
Inscribed Polygon
All the vertices of the polygon lie on the circle. (Page- 674)
Circumscribed circle
The circle that contains the vertices of the inscribed polygon. (Page- 674)
Theorem 10.9
If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle. (Page- 674)
Theorem 10.10
A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. (Page- 675)
Theorem 10.11
If a tangent and a chord intersect at a point of a circle, then the measure of each angle formed is ½ the measure it its intercepted arc. (Page- 680)
Intersecting Lines and Circles
If 2 lines intersect a circle, there are 3 places where the lines can intersect:
1. On the circle
2. Inside the circle
3. Outside the circle
Angles Inside the Circle Theorem
If 2 chords intersect inside a circle, then the measure of each angle is ½ the sum of the measures of the arcs intercepted by the angle and its vertical angle. (Page- 681)
Angles Outside Theorem
If a tangent and a secant, 2 tangents, or 2 secants intersect outside of a circle, then the measure of the angle formed is ½ the difference of the measures of the intercepted arcs. (Page- 681)
Segments of the Chord
When 2 chords intersect in the interior of a circle, each chord is divided into 2 segments that are called segments of the chord. (Page- 689)
Segments of Chords Theorem
If 2 chords intersect in the interior of a circle, then the product of the lengths of the segments of 1 chord is equal to the product of the lengths of the segments of the other chord. (Page- 689)
Secant Segment
A segment that contains a chord of a circle, and has exactly one endpoint outside the circle. (Page- 690)
External Segment
The part of the secant segment that is outside the circle. (Page- 690)
Segments of Secants Theorem
If 2 segments share the same endpoint outside a circle, then the product of the lengths of 1 secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment. (Page- 690)
Segments of Secants and Tangents Theorem
If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the lengths of the secant segment and its external segments equals the square of the length of the tangent segment. (Page- 691)
Locus
The set of all points in a plane that satisfy a given condition or a set of given conditions. (Page- 697)
Standard Equation of a Circle
The standard equation of a circle with the center (h,k) and the radius r is- (x-h)^2 + (y-k)^2 = r^2 (Page- 699)

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