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Definition
A circle is the set of all points in a plane that are the same distance from a fixed point called the center. The fixed distance is called the radius. Important parts of a circle include the diameter (twice the radius), chord (a line segment joining two points on the circle), arc (a part of the circle’s circumference), sector (a region formed by two radii and an arc), and tangent (a line that touches the circle at exactly one point).
Circle theorems are geometric rules that describe relationships between angles, lines, and points in a circle. These theorems help us solve problems involving angles and lengths inside and around circles.
Summary
Angle at the Center Theorem
The angle formed at the center of a circle is twice the angle formed at the circumference by the same arc.
Angle in a Semicircle Theorem
An angle formed in a semicircle is always 90° (a right angle).
Angles in the Same Segment Theorem
Angles subtended by the same arc at the circumference are equal.
Opposite Angles in a Cyclic Quadrilateral
The opposite angles of a quadrilateral inscribed in a circle add up to 180°.
Tangent–Radius Theorem
A tangent to a circle is perpendicular to the radius at the point of contact.
Alternate Segment Theorem
The angle between a tangent and a chord through the point of contact is equal to the angle in the opposite arc.
Circle and Its Theorems Math Activities
This is a fantastic bundle which includes 10 activities with answer guides about Circle and Its Theorems. All our worksheets are completely editable so can be tailored for your curriculum and target audience.
Resource Examples
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Worksheets Activities Included
- Parts of a Circle Exploration
- Angle at the Center Theorem
- Inscribed Angle Theorem
- Angle in a Semicircle
- Tangent–Radius Theorem
- Two Chords Intersecting Inside a Circle
- Two Secants from an External Point
- Tangent–Secant Theorem
- Opposite Angles of a Cyclic Quadrilateral
- Arc Length and Sector Area