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Chapter 10 Axioms
9.2, 10.1-10.9 Circle Theorems and Definitions
| Question | Answer |
|---|---|
| A ______________ is the set of all points in a plane that are a given distance from a given point in the plane | Circle |
| The point that names the circle is the ________________ of the circle | Center |
| The distance from the center of a circle to the circle is the __________________ | Radius |
| A ___________ is the chord that passes through the center of the circle | Diameter |
| A ______ is equal in length to two radii | diameter |
| All radii of the same circle are _____. (p 439 theorem) | congruent |
| The circumference of a circle = _____ | d*pi |
| The area of a circle = _____ | r2*pi |
| The length of an arc = _____ | %C |
| The % is the measure of the arc divided by 360. | |
| The area of a sector = _____ | % A |
| The % is the measure of the arc divided by 360. | |
| Two or more coplanar circles with the same center are called _____________________ circles | concentric |
| A point is ____________ (in the ____________ of) a circle if its distance from the center is less than the radius | Inside; interior |
| A point is _____________ (in the ____________ of) a circle if its distance from the center is greater than the radius | Outside exterior |
| A point is _____a circle if its distance from the center is equal to the radius | Equidistant |
| A _____ of a circle is a segment joining any 2 points on the circle | chord |
| A _____ of a circle is a chord that passes through the center of the circle | diameter |
| The distance from the center of a circle to a chord is the measure of the __________________ segment from the center to the chord | perpendicular |
| If a radius is perpendicular to a chord then | The radius bisects the chord |
| If a radius of a circle bisects a chord that is not a diameter then | It is perpendicular to that chord |
| The _____ of a chord passes through the center of a circle | Perpendicular bisector |
| If 2 chords of a circle are equidistant from the center of a circle then ___ | The chords are congruent |
| If 2 chords of a circle are congruent then ____ | They are equidistant |
| An _____ consists of 2 points on a circle and all points on the circle needed to connect the points by a single path | arc |
| The _____of an arc is the center of the circle of which the arc is a part. The unit is _____ | Measure degrees |
| A _____ is an angle whose vertex is at the center of a circle | central |
| A _____is an arc whose points are on or between the sides of a central angle | Minor arc |
| A _____ is an arc whose points are on or outside of a central angle | Major arc |
| A _____ is an arc whose endpoints are the endpoints of a diameter | semicircle |
| The measure of a minor arc or a semicircle is _____the measure of the central angle that intercepts the arc | Same as |
| The measure of a major arc is 360 minus the measure of _______ _______________ ______ with the same endpoints | The minor arc |
| Two arcs are ________________ whenever they have the same measure and are parts of the same circle or congruent circles | Congruent |
| If 2 central angles of a circle (or of congruent circles) are congruent then | Their intercepted arcs are congruent |
| If 2 arcs of a circle (or of congruent circles) are congruent then | The corresponding central angles are congruent |
| If 2 central angles of a circle (or of congruent circles) are congruent then | The corresponding chords are congruent |
| If 2 chords of a circle (or of congruent circles) are congruent then | The corresponding central angles are congruent |
| If 2 arcs of a circle (or of congruent circles) are congruent then | The corresponding chords are congruent |
| If 2 chords of a circle (or of congruent circles) are congruent then | The corresponding arcs are congruent |
| A __________________ is a line that intersects a circle at exactly 2 points. (Every ______________ contains a chord of the circle.) | Secant |
| A ________________ is a line that intersects a circle at exactly _________ point. This point is called the _________________ ____ ________________ or point of contact | Tangent; point of tangency |
| A tangent line is ____________ drawn to the point of contact. | Perpendicular to the radius |
| If a line is perpendicular to a radius at its outer endpoint then | It is tangent to the circle |
| A ___________________________ ______________________________ is the part of a tangent line between the points of contact and a point outside the circle | Tangent segment |
| A __________________________ _______________________________ is the part of a secant line that joins a point outside the circle to the farther intersection point of the secant and the circle | Secant segment |
| The ________________________ ____________________________ of a secant segment is the part of a secant line that joins the outside point to the nearer intersection point | External part |
| If 2 tangent segments are drawn to a circle from an external point then | Those segments are congruent |
| __________________________ ________________________ are circles that intersect each other at exactly one point | Tangent circles |
| Two circles are ________________________ _______________________ if each of the tangent circles lies outside the other | Externally tangent |
| Two circles are __________________________________ ______________________ if one of the tangent circles lies inside the other | Internally tangent |
| An _____________________ ___________________ is an angle whose vertex is on a circle and whose sides are determined by 2 chords | Inscribed angle |
| A _________________________________ angle is an angle whose vertex is on a circle and whose sides are determined by a tangent and a chord that intersect at the tangent's point of contact | Tangent-chord angle |
| The measure of an inscribed angles or a tangent-chord angle (vertex on a circle) is | ½ the measure of its intercepted arc |
| A ______________________________ angle is an angle formed by 2 chords that intersect inside a circle but not at the center | Chord-chord angle |
| The measure of a chord-chord angle is | ½ the sum of the measures of the arcs intercepted by the chord-chord angle and its vertical angle |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 secants | Secant-secant angle |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by a secant and a tangent | Secant-tangent angle |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 tangents | Tangent-tangent angle |
| The measure of a secant-secant angle a secant-tangent angle or a tangent-tangent angle (vertex outside the circle) is | ½ the difference of the measures of the intercepted arcs |
| If 2 inscribed or tangent-chord angles intercept the same arc then | They are congruent |
| If the vertex of the angle is ____ the circle | Then use this formula to find the angle’s measure: |
| Center | Arc |
| IN | (Arc + arc)/2 |
| ON | (arc)/2 |
| OUT | (arc-arc)/2 |
| If 2 inscribed or tangent-chord angles intercept congruent arcs then | They are congruent |
| An angle inscribed in a semi- circle is a ____________________ ___________________. | Right angle |
| The sum of the measures of a tangent-tangent angle and its minor arc is __________________. | 180 degrees |
| A polygon is __________________ ___________ a circle if all of its vertices lie on the circle | Inscribed in |
| A polygon is _____________ ___________ a circle if each of its sides is tangent to the circle | Circumscribed about |
| The center of a circle circumscribed about a polygon is the ____________________________ of the polygon | Circumcenter |
| The center of a circle inscribed in a polygon is the _______________________ of the polygon | Incenter |
| If a quadrilateral is inscribed in a circle | Its opposite angles are supplementary |
| If a parallelogram is inscribed in a circle | Then the polygon formed is a rectangle |
| If 2 chords of a circle intersect inside the circle then | Part*part = Part*part |
| If a tangent segment and a secant segment are drawn from an external point to a circle then | Outside*whole = Outside*whole (One side squared) |
| If 2 secant segments are drawn from an external point to a circle then | Outside*whole = Outside*whole |
| The circumference of a circle is | Its perimeter |
| The formula for the circumference of a circle is . | Diameter*pi |
| The length of an arc is equal to | Circumference*fractional part of circle determined by arc |
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vespaj26
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