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 definition of a chord?

Back

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

Front

What is the definition of a tangent?

Back

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

Front

What is the definition of a radius?

Back

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

Front

What is the definition of a diameter?

Back

A diameter is a chord that passes through the center of the circle, and it is twice the length of the radius.

Front

If two angles subtend the same arc, what can be said about them?

Back

The angles are equal.

Front

What is the angle at the center of a circle compared to the angle at the circumference subtending the same arc?

Back

The angle at the center is twice the angle at the circumference.

Front

What is the relationship between the angles formed by two intersecting chords?

Back

The angles are equal to half the sum of the measures of the arcs intercepted by the angles.

Front

What is the relationship between the angles formed by a tangent and a chord?

Back

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

Front

What is the angle in a semicircle?

Back

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