Podcast
Questions and Answers
What is the relationship between the circumference and the diameter of a circle?
What is the relationship between the circumference and the diameter of a circle?
How is the area of a circle calculated in terms of its radius?
How is the area of a circle calculated in terms of its radius?
What can be inferred if a diameter is perpendicular to a chord in a circle?
What can be inferred if a diameter is perpendicular to a chord in a circle?
What is the measure of an inscribed angle in a semicircle?
What is the measure of an inscribed angle in a semicircle?
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What is true about angles in the same segment of a circle?
What is true about angles in the same segment of a circle?
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What does it mean if two chords in a circle are equidistant from the center?
What does it mean if two chords in a circle are equidistant from the center?
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What is the relationship between the angle at the center of a circle and the inscribed angle subtended by the same arc?
What is the relationship between the angle at the center of a circle and the inscribed angle subtended by the same arc?
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What is true about the lengths of tangents drawn from an external point to a circle?
What is true about the lengths of tangents drawn from an external point to a circle?
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Study Notes
Circles
- A circle is a two-dimensional geometric shape consisting of all points in a plane that are at a constant distance from a central point.
- This constant distance is called the radius.
- A line segment that passes through the center of the circle and has endpoints on the circle is called a diameter. The diameter is twice the radius.
- A line segment connecting any two points on the circle is called a chord.
- A chord that passes through the center of the circle is a diameter.
- A line segment from the center of the circle to a point on the circle is a radius.
Circumference Formulas
- The circumference of a circle is the distance around the circle.
- The formula for the circumference of a circle in terms of the radius (r) is C = 2πr.
- The formula for the circumference of a circle in terms of the diameter (d) is C = πd.
Area Calculation
- The area of a circle is the amount of space enclosed by the circle.
- The formula for the area of a circle in terms of the radius (r) is A = πr².
Properties of Chords
- If a diameter is perpendicular to a chord, then it bisects the chord and its arc.
- Two chords are equidistant from the center if and only if they are congruent.
- A line that bisects a chord (not a diameter) and is perpendicular to the chord passes through the center of the circle.
Inscribed Angles
- An inscribed angle is an angle formed by two chords that have a common endpoint on the circle.
- The measure of an inscribed angle is half the measure of its intercepted arc.
- Inscribed angles that intercept the same arc are congruent.
- An angle inscribed in a semicircle is a right angle.
Circle Theorems
- The angle at the center is twice the angle at the circumference subtended by the same arc.
- Angles in the same segment are equal.
- The opposite angles of a cyclic quadrilateral sum to 180 degrees.
- The tangent to a circle is perpendicular to the radius drawn to the point of contact.
- The lengths of tangents from an external point to a circle are equal.
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Description
This quiz covers the basics of circles, including their definitions, formulas for circumference and area, and key terms such as radius, diameter, and chord. Test your understanding of these geometric concepts and their applications.
