Circle Theorems

Front

What is a circle theorem?

Back

Circle theorems are rules that describe the relationships between angles, arcs, and lines in circles.

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

The angle in a semicircle is a right angle (90 degrees).

Tags

CCSS.HSG.C.A.2

Front

What is the tangent to a circle?

Back

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

Front

What is the relationship between a tangent and a radius?

Back

A tangent to a circle is perpendicular to the radius at the point of contact.

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

What is the inscribed angle theorem?

Back

The inscribed angle theorem states that an angle inscribed in a circle is half the measure of the central angle that subtends the same arc.

Tags

CCSS.HSG.C.A.2

Front

What is the cyclic quadrilateral theorem?

Back

In a cyclic quadrilateral, the opposite angles are supplementary (add up to 180 degrees).

Front

What is the chord theorem?

Back

The perpendicular from the center of a circle to a chord bisects the chord.

Tags

CCSS.HSG.C.A.2