Circle Theorems

Front

What is a circle theorem?

Back

Circle theorems are theorems that describe the properties and relationships of angles, arcs, and chords in a circle.

Tags

CCSS.HSG.C.A.2

Front

What is the angle at the center of a circle?

Back

The angle at the center of a circle is twice the angle at the circumference subtended by the same arc.

Tags

CCSS.HSG.SRT.C.8

Front

What is the relationship between angles in the same segment of a circle?

Back

Angles in the same segment of a circle are equal.

Tags

CCSS.HSG.C.A.2

Front

What is the angle in a semicircle?

Back

An angle inscribed in a semicircle is a right angle (90 degrees).

Tags

CCSS.HSG.C.A.2

Front

What is the tangent-secant theorem?

Back

The tangent-secant theorem states that the square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external part.

Tags

CCSS.HSG.C.A.2

Front

What is the chord-chord product theorem?

Back

The chord-chord product theorem states that if two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal.

Tags

CCSS.HSG.C.A.2

Front

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

Back

The radius drawn to the point of contact is perpendicular to the tangent at that point.

Front

What is the inscribed angle theorem?

Back

The inscribed angle theorem states that the measure of an inscribed angle is half the measure of the intercepted arc.

Tags

CCSS.HSG.C.A.2

Front

What is the alternate segment theorem?

Back

The alternate segment theorem states that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

Tags

CCSS.HSG.C.A.2

Front

How do you find the length of an arc?

Back

The length of an arc can be found using the formula: Length = (θ/360) * 2πr, where θ is the angle in degrees and r is the radius.

Tags

CCSS.HSG.C.B.5