Circle Theorems

Click on the flashcard to see the answer



What is the central angle of a circle?

The central angle is an angle whose vertex is the center of the circle and whose sides are radii.

What does the Inscribed Angle Theorem state?

The Inscribed Angle Theorem states that an inscribed angle is half the measure of the central angle that subtends the same arc.

What is the relationship between the radius and a tangent at the point of tangency?

The radius is perpendicular to the tangent at the point of tangency.

What does the Alternate Segment Theorem describe?

The Alternate Segment Theorem states that the angle between a chord and a tangent is equal to the angle in the alternate segment.

What are congruent chords?

Congruent chords in a circle are chords that are equal in length.

What does the Perpendicular Bisector Theorem state in relation to chords?

It states that the perpendicular bisector of a chord passes through the center of the circle.

What is a cyclic quadrilateral?

A cyclic quadrilateral is a four-sided figure where all vertices lie on the circumference of a circle.

What is the property of the opposite angles of a cyclic quadrilateral?

The opposite angles of a cyclic quadrilateral add up to 180 degrees.

What is the Arc Addition Postulate?

The Arc Addition Postulate states that the measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

What is the Angle at the Center Theorem?

The Angle at the Center Theorem states that the angle subtended at the center is twice that subtended at any point on the circle.

What is the significance of equal arcs in a circle?

Equal arcs in a circle subtend equal angles at the center and equal inscribed angles at the circumference.

What is the Tangent-Secant Theorem?

The Tangent-Secant Theorem states that if a tangent and a secant are drawn from an external point, the square of the tangent is equal to the product of the entire secant segment and its external part.

What is a semicircle and how is it related to angles?

A semicircle is half a circle formed by a diameter. An angle inscribed in a semicircle is a right angle.

What does the Chord Segment Theorem state?

The Chord Segment Theorem states that when two chords intersect, the products of the lengths of their segments are equal.

What does the Tangent-Tangent Theorem state?

The Tangent-Tangent Theorem states that two tangent segments drawn from an external point to a circle are equal in length.





Test Your Knowledge

Select the correct option


1. What is the central angle of a circle?

The central angle is an angle whose vertex is the center of the circle and whose sides are radii.

An angle formed by intersecting chords within the circle.

An angle formed by two tangents drawn from an external point.

An angle adjacent to a central vertex.

2. What does the Inscribed Angle Theorem state?

An inscribed angle is equal to the measure of the arc it subtends.

An inscribed angle is twice the measure of the minor arc it subtends.

An inscribed angle is the same as a central angle subtending the same arc.

The Inscribed Angle Theorem states that an inscribed angle is half the measure of the central angle that subtends the same arc.

3. What is the relationship between the radius and a tangent at the point of tangency?

The radius is perpendicular to the tangent at the point of tangency.

The radius bisects the tangent at the point of tangency.

The radius is parallel to the tangent at the point of tangency.

The radius forms an acute angle with the tangent at the point of tangency.

4. What does the Alternate Segment Theorem describe?

The Alternate Segment Theorem states that the angle between a chord and a tangent is equal to the angle in the alternate segment.

The Alternate Segment Theorem describes equal segments within a circle.

The theorem states that alternate angles on a segment are equal.

The Alternate Segment Theorem connects congruent tangent segments to the circle.

5. What are congruent chords?

Congruent chords in a circle are chords that are equal in length.

Chords that have perpendicular bisectors passing through the center.

Chords which subtend equal angles at the center of the circle.

Chords which are tangents to the circle at the endpoints.

6. What does the Perpendicular Bisector Theorem state in relation to chords?

The perpendicular bisector of a chord divides the chord into two equal arcs.

Theorem states the perpendicular bisector of a chord forms two right angles with it.

It states that the perpendicular bisector of a chord passes through the center of the circle.

The theorem establishes the equal length of radii formed by the bisector.

7. What is a cyclic quadrilateral?

A four-sided figure inscribed in a triangle.

A quadrilateral with equal sides inscribed outside a circle.

A cyclic quadrilateral is a four-sided figure where all vertices lie on the circumference of a circle.

A quadrilateral in which only one pair of opposite angles are supplementary.

8. What is the property of the opposite angles of a cyclic quadrilateral?

The opposite angles of a cyclic quadrilateral add up to 180 degrees.

The opposite angles are always right angles.

The opposite angles are congruent.

The opposite angles add up to 360 degrees.

9. What is the Arc Addition Postulate?

The Arc Addition Postulate states that the sum of the arc length and chord length is constant.

The Arc Addition Postulate involves adding the angles subtended by different arcs.

The Arc Addition Postulate declares the arc length doubling with arc additions.

The Arc Addition Postulate states that the measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

10. What is the Angle at the Center Theorem?

Theorem where an angle at the center is bisected by each radius.

Theorem where angles at the center and circumference are congruent.

The Angle at the Center Theorem states that the angle subtended at the center is twice that subtended at any point on the circle.

Theorem regarding the equal division of the circle's angles by the central axis.

11. What is the significance of equal arcs in a circle?

Equal arcs create isosceles triangles with the same base length.

Equal arcs in a circle subtend equal angles at the center and equal inscribed angles at the circumference.

Equal arcs are opposite sides of any inscribed quadrilateral.

Equal arcs result in parallel tangents.

12. What is the Tangent-Secant Theorem?

The theorem states two secants drawn from the same external point are equal.

The theorem asserts that the tangents of segments from different points are equal.

The theorem involves chords and tangents forming a perfect semicircle.

The Tangent-Secant Theorem states that if a tangent and a secant are drawn from an external point, the square of the tangent is equal to the product of the entire secant segment and its external part.

13. What is a semicircle and how is it related to angles?

A semicircle forms an equilateral triangle when connected with the circle's center.

A semicircle ensures all inscribed angles are obtuse.

A semicircle is half a circle formed by a diameter. An angle inscribed in a semicircle is a right angle.

A semicircle forms a perfect arch, doubling all subtended angles.

14. What does the Chord Segment Theorem state?

The theorem states that each chord divides the circle into two equal segments.

The Chord Segment Theorem states that when two chords intersect, the products of the lengths of their segments are equal.

It claims intersecting chords form equal angles with circle radius.

It recognizes all intersecting chords as inherently congruent.

15. What does the Tangent-Tangent Theorem state?

The Tangent-Tangent Theorem states that two tangent segments drawn from an external point to a circle are equal in length.

The theorem implies tangents are always perpendicular to each other.

The theorem states opposite tangents on the circle are equidistant from a point.

The theorem claims tangential triangles have equal internal angles.