A circle is the set of all points in a plane that are the same distance from a given point, called the center. Center. Definition: A circle is the set of all points on a plane that is a fixed distance from the center.

Definition: A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle.

In geometry, a locus (plural: loci) (Latin word for “place”, “location”) is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.

Chapter 6 Vocabulary – Geometry

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The center of a circle is also called the focus of the circle.

In case of a circle, a secant is a line that intersects the circle exactly twice. The line segment joining the two points where the secant intersects the circle is a chord. If the secant passes through the centre of the circle, the line segment joining the two points of intersection is a diameter.

The word secant comes from the Latin word secare, meaning to cut. In the case of a circle, a secant will intersect the circle at exactly two points.

Theorem: Angle at the centre of a circle is twice the size of the angle at the circumference. If an arc subtends an angle at the centre of a circle and at the circumference, then the angle at the centre is twice the size of the angle at the circumference.

• Circle Theorem 1 – Angle at the Centre.
• Circle Theorem 2 – Angles in a Semicircle.
• Circle Theorem 3 – Angles in the Same Segment.
• Circle Theorem 4 – Cyclic Quadrilateral.
• Circle Theorem 5 – Radius to a Tangent.
• Circle Theorem 6 – Tangents from a Point to a Circle.
• Circle Theorem 7 – Tangents from a Point to a Circle II.

First circle theorem – angles at the centre and at the circumference. Second circle theorem – angle in a semicircle. Third circle theorem – angles in the same segment.

Circle theorem may refer to: Any of many theorems related to the circle; often taught as a group in GCSE mathematics. Thales’ theorem, if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle. Alternate segment theorem. Ptolemy’s theorem.

Specifically, given a chain of six circles all tangent to a seventh circle and each tangent to its two neighbors, the three lines drawn between opposite pairs of the points of tangency on the seventh circle all pass through the same point.

The opposite angles in a cyclic quadrilateral add up to In plain terms: If you look at the cyclic quadrilateral (a four sided shape where the four vertices touch the circumference of a circle) below, each vertex is a point on the circumference of the circle.

In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. The full arc of a semicircle always measures 180° (equivalently, π radians, or a half-turn).

The semicircle is also referred to as a half-disk. Since the semicircle is half of the circle (360 degrees), the arc of the semicircle always measures 180 degrees….Formulas to Remember.

FAQs on Semicircle Formulas It is expressed as, Area of a Semicircle formula = πR2/ 2. Where, r = R is the radius of a semicircle. π(pi) is 3.142 approximately.

A semicircle whose diameter is 20 cm will have area of 157 cm²