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Ch 10 Circle
Geometry for Enjoyment and Challenge
| Question | Answer |
|---|---|
| A ______________ is the set of all points in a plane that are a given distance from a given point in the plane. (p 439 definition) | 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 = _____ | Diameter* pi or twice radius * pi |
| The area of a circle = _____ | radius squared times pi |
| The length of an arc = _____ | %C where the % is the measure of the arc divided by 360. |
| The area of a sector = _____ | % A where the % is the measure of the arc divided by 360. |
| Two or more coplanar circles with the same center are called _____________________ circles. (p 439 definition) | Concentric |
| A point is ____________ (in the ____________ of) a circle if its distance from the center is less than the radius. (p 439 definition) | |
| A point is _____________ (in the ____________ of) a circle if its distance from the center is greater than the radius. (p 439 definition) | Outside exterior |
| A point is _____a circle if its distance from the center is equal to the radius. (p 440 definition) | 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. | |
| 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 the chord |
| The _____ of a chord passes through the center of a circle. | |
| 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. | |
| A _____ is an arch whose points are on or outside of a central angle. | |
| 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. | |
| The measure of a major arc is 360 minus the measure of _______ _______________ ______ with the same endpoints. | |
| Two arcs are ________________ whenever they have the same measure and are parts of the same circle or congruent circles. | |
| If 2 central angles of a circle (or of congruent circles) are congruent then | |
| If 2 arcs of a circle (or of congruent circles) are congruent then | |
| If 2 central angles of a circle (or of congruent circles) are congruent then | |
| If 2 chords of a circle (or of congruent circles) are congruent then | |
| If 2 arcs of a circle (or of congruent circles) are congruent then | |
| If 2 chords of a circle (or of congruent circles) are congruent then | |
| A __________________ is a line that intersects a circle at exactly 2 points. (Every ______________ contains a chord of the circle.) | |
| 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 to the radius drawn to the point of contact. | |
| If a line is perpendicular to a radius at its outer endpoint then | |
| Such a tangent is a ___ if it lies between the circles (intersects the segment joining the centers) or a ___ if it is not between the circles (does not intersect the segment joining the centers). | |
| A ______is the part of a tangent line between the points of contact and a point outside the circle. | |
| 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. | |
| The ___ of a secant segment is the part of a secant line that joins the outside point to the nearer intersection point. | |
| If 2 tangent segments are drawn to a circle from an external point then | |
| ___ are circles that intersect each other at exactly one point. | |
| Two circles are ___________ if each of the tangent circles lies outside the other. | |
| Two circles are ___________if one of the tangent circles lies inside the other. | |
| A _____is a line tangent to two circles (not necessarily at the same point). | |
| An ___________________ is an angle whose vertex is on a circle and whose sides are determined by 2 chords. | |
| 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. | |
| The measure of an inscribed angles or a tangent-chord angle (vertex on a circle) is | |
| A ______________________________ angle is an angle formed by 2 chords that intersect inside a circle but not at the center. | |
| The measure of a chord-chord angle is | |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 secants. | |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by a secant and a tangent. | |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 tangents. | |
| The measure of a secant-secant angle a secant-tangent angle or a tangent-tangent angle (vertex outside the circle) is | |
| . | |
| If 2 inscribed or tangent-chord angles intercept the same arc then | |
| . | |
| Complete the chart below. In class I provided a summary on the board; this is how I anticipate you will complete the chart. (Hint: I pointed out the top of page 472 when I completed it in class.) | |
| 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 | |
| . | |
| An angle inscribed in a semi- circle is a ____________________ ___________________. | |
| The sum of the measures of a tangent-tangent angle and its minor arc is __________________. | |
| A polygon is __________________ ___________ a circle if all of its vertices lie on the circle. | |
| A polygon is _____________ ___________ a circle if each of its sides is tangent to the circle. | |
| The center of a circle circumscribed about a polygon is the ____________________________ of the polygon. | |
| The center of a circle inscribed in a polygon is the _______________________ of the polygon. | |
| If a quadrilateral is inscribed in a circle | |
| . | |
| If a parallelogram is inscribed in a circle | |
| . | |
| If 2 chords of a circle intersect inside the circle then | |
| . | |
| If a tangent segment and a secant segment are drawn from an external point to a circle then | |
| . | |
| If 2 secant segments are drawn from an external point to a circle then | |
| . | |
| The of a circle is its perimeter. | |
| The formula for the circumference of a circle is . | |
| The length of an arc is equal to | |
| . |
Created by:
Mira Kresovic
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