Line QO is best described as a radius.

A radius is a line segment from the center of the circle to a point on the circle.

Line OR is best described as a radius.

A radius is a line segment from the center of the circle to a point on the circle.

A line, ray, or segment that is tangent to two coplanar circles.

A line is tangent to a circle if it is perpendicular to a radius of the circle at its endpoint on the circle.

Tangent segments from a common external point are congruent.

A line is tangent to a circle if it is perpendicular to a radius of the circle at its endpoint on the circle.

Diagram showing a circle with a triangle formed by points S, T, and P.

Determine if line ST is tangent to circle P by checking if $$ST^2 = SP^2 + TP^2$$ .

Determine if line DE is tangent to circle C.

Check if $$$CD^2 + CE^2 = DE^2$$$ .

A minor arc is smaller than a semicircle.

A semicircle is an arc that represents half of a circle.

Illustration of a circle with a chord cutting through it, forming an arc.

Circle with points A, B, C, and D. Chord AB and chord AC are shown with equal segments marked as 9.

If m∠AB = 110°, then m∠BC can be determined using the properties of angles in a circle. If m∠AC = 150°, then m∠AB can be determined using the properties of angles in a circle.

If a diameter bisects a chord, then the diameter is perpendicular.

This property indicates that a diameter that divides a chord into two equal parts must intersect the chord at a right angle.

Diagram of a circle with points A, B, C, D, E, F. Angles marked as 9x° and (80 - x)°.

Calculate the length of CE using the given angles and circle properties.

Segments of Chords Theorem

If two chords intersect in the interior of a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

A secant segment is a segment that contains a chord of a circle and has exactly one endpoint outside the circle.

Diagram of two secant segments intersecting outside a circle

The diagram illustrates the relationship: EA \cdot EB = EC \cdot ED.

Theorem 10.20: Segments of Secants and Tangents Theorem

If a secant segment and a tangent segment share an endpoint outside a circle, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.

Diagram of a circle with a tangent and a secant line, labeled with numbers 5, 7, and x.

Value of x using the tangent-secant theorem. Diagram included.

Find the value of x in the given geometric figure with a circle and triangle.

Use the Pythagorean theorem to solve for x: $$x^2 + 5^2 = 6^2$$ .

Circle with chords ML and JK intersecting at N. ML = x + 2 and x + 1, JK = x and x + 4.

Lengths of ML and JK can be found using the intersecting chords theorem.

Circle with intersecting chords labeled: x, 6, 4, 3

Use the intersecting chords theorem: (x)(6) = (4)(3)

Circle Geometry Terms Flashcards

Student preview

30 questions

Show all answers

1.

FLASHCARD QUESTION

Front

The set of all points in a plane that are equidistant from a given point.

Back

Circle

2.

FLASHCARD QUESTION

Front

A segment whose endpoints are the center and any point on the circle.

Back

Radius

3.

FLASHCARD QUESTION

Front

The center of the circle is labeled as S.

Back

S is the point from which all points on the circle are equidistant.

4.

FLASHCARD QUESTION

Front

The chord of the circle is labeled as segment EH.

Back

A chord is a line segment with both endpoints on the circle.

5.

FLASHCARD QUESTION

Front

Line PR is best described as a tangent.

Back

A tangent is a line that touches a circle at exactly one point.

6.

FLASHCARD QUESTION

Front

Line MN is best described as a secant.

Back

A secant is a line that intersects a circle at two points.

7.

FLASHCARD QUESTION

Front

Line PQ is best described as a chord.

Back

A chord is a line segment whose endpoints lie on the circle.

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