Circle Unit Flashcards
Defien Circle
The set of all points a fixed distance from a given center point.
Define radius
The distance from the center to any point on the circle
How do you name a circle?
Using the symbol for circle followed by the center
Define chord
A line segment with both endpoints on the circle.
What do you call the longest possible chord?
The diameter
What is the relationship between the length of the radius and the diameter?
The length of the radius is half the length of the diameter. The length of the diameter is twice the length of the radius.
Define secant
A line, ray, or segment that contains a chord
What are two concentric circles?
Two circles with the same center
What are 2 congruent circles?
2 circles with congruent radii
Define tangent.
A line, ray, or segment that intersects a circle at only 1 point.
What is the relationship between a tangent and the radius at the point of tangency?
They are perpendicular.
What is true about two tangent segments from the same external point?
They are congruent.
What is true about the segment from the center to that same external point from which 2 tangent segments are made?
It bisects the angle made by the tangents and the radii
How can you tell if a tangent segment between 2 circles is internal or external?
It is internal if it intersects the segment that connects the centers of the 2 circles. Otherwise it is external
Two tangent circles have what in common?
The point of tangency
What is the difference between two circles that are internally tangent and two that are externally tangent?
If 2 circles are internally tangent, one circle is contained within the other except for the point of tangency. If they are externally tangent, the 2 circles are outside each other except for the point of tangency.
What is the definition of an inscribed circle?
A circle inside a circumscribed polygon
What is significant about the sides of a polygon that is circumscribed?
They are all tangents
What is the definition of a circumscribed circle?
A circle with an inscribed polygon
What is significant about the sides of a polygon that is inscribed?
They are all chords
How are arcs measured?
In degrees
What are 2 congruent arcs?
Two arcs with the same measure
What are the 3 types of arcs?
Minor arc, semicircle, major arc
How do we name arcs?
Minor arc - The 2 endpoints with the arc symbol above it
Semicircle & major arc
The 2 endpoints with one other point that the arc goes through in the middle, with the arc symbol above it.
The endpoints of a semicircle are also the endpoints of what?
A diameter
What is a central angle?
An angle with vertex at the center and with sides that are radii
What is the rule about the measure of a central angle and its intercepted arc?
They have the same measure
Congruent chords will also make what?
Congruent arcs
What is an inscribed angle?
An angle with vertex on the circle and sides made by chords
What is the rule between an inscribed angle and its intercepted arc?
The measure of the angle is half the measure of its intercepted arc.
If a quadrilateral is inscribed in a circle, then what is true about its angles?
The opposite angles are supplementary.
If an inscribed angle intercepts a semicircle, what is true?
It is a right angle.
What is true about the arcs between two parallel segments?
They are congruent.
What is the rule for the angle formed by two chords that intersect inside a circle, in relation to its intercepted arcs?
The measure of the angle equals the measure of the big arc plus the measure of the little arc, divided by 2
What is the rule about the angles formed by a tangent and chord that intersect on a circle, in relation to its intercepted arcs?
The measure of the angle is half the measure of its intercepted arc.
What is the rule for the angle formed by two secants/tangents that intersect outside a circle, in relation to its intercepted arcs?
The measure of the angle equals the measure of the big arc minus the measure of the little arc, divided by 2
