Podcast
Questions and Answers
In the same circle, or in congruent circles, two chords are congruent if and only if they are _________________ from the center.
In the same circle, or in congruent circles, two chords are congruent if and only if they are _________________ from the center.
equidistant
A __________ is an angle whose sides are tangent to a circle.
A __________ is an angle whose sides are tangent to a circle.
circumscribed
A(n) _______ angle is an angle whose vertex is on the circle, and whose sides contain chords of the circle.
A(n) _______ angle is an angle whose vertex is on the circle, and whose sides contain chords of the circle.
inscribed
A ______ angle is an angle whose vertex is at the center of the circle.
A ______ angle is an angle whose vertex is at the center of the circle.
A _________ is the set of all points in a plane equidistant from a given point.
A _________ is the set of all points in a plane equidistant from a given point.
Two circles with the same center are called ____________ circles.
Two circles with the same center are called ____________ circles.
An arc of a circle with a measure of 180 degrees is a ____________.
An arc of a circle with a measure of 180 degrees is a ____________.
A _______ arc of a circle has a measure of less than 180 degrees.
A _______ arc of a circle has a measure of less than 180 degrees.
A _______ arc of a circle has a measure of more than 180 degrees.
A _______ arc of a circle has a measure of more than 180 degrees.
A polygon is an inscribed polygon when all its ________ are on the circle.
A polygon is an inscribed polygon when all its ________ are on the circle.
An arc that lies between two lines, rays, or segments is called an _____ arc.
An arc that lies between two lines, rays, or segments is called an _____ arc.
Tangent segments from a common exterior point are _______.
Tangent segments from a common exterior point are _______.
A(n) _______ segment is the part of a secant segment that is outside the circle.
A(n) _______ segment is the part of a secant segment that is outside the circle.
A quadrilateral can be inscribed in a circle if and only if its opposite angles are _________.
A quadrilateral can be inscribed in a circle if and only if its opposite angles are _________.
Two circles are ________ if and only if they have the same radius.
Two circles are ________ if and only if they have the same radius.
If one side of an inscribed triangle is a _______ of a circle, then the triangle is a right triangle.
If one side of an inscribed triangle is a _______ of a circle, then the triangle is a right triangle.
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Study Notes
Circle Theorems and Definitions
- Two chords in the same or congruent circles are congruent if they are equidistant from the center.
- A circumscribed angle has sides that are tangent to a circle.
- An inscribed angle has its vertex on the circle, with sides that contain chords of the circle.
- A central angle has its vertex at the center of the circle.
Circle Properties
- A circle is defined as the set of all points in a plane that are equidistant from a given point (the center).
- Circles that share the same center are referred to as concentric circles.
- An arc measuring 180 degrees is known as a semicircle.
Types of Arcs
- A minor arc measures less than 180 degrees.
- A major arc measures more than 180 degrees.
- An intercepted arc lies between two lines, rays, or segments.
Inscribed Polygons and Quadrilaterals
- A polygon is inscribed in a circle if all its vertices lie on the circle.
- A quadrilateral can be inscribed in a circle only if its opposite angles are supplementary.
Segments and Congruence
- Tangent segments drawn from a common external point to a circle are congruent.
- An external segment of a secant is the part that lies outside the circle.
Triangle Properties in Circles
- An inscribed triangle is a right triangle if one of its sides is a diameter of the circle.
- Two circles are congruent if they have the same radius.
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