Maths circle theorums

What is the circle theorem?

A circle theorem is a mathematical statement that describes the properties and relationships related to circles.

The angle at the center of a circle theorem states that:

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

What is the cyclic quadrilateral theorem?

In any cyclic quadrilateral, the sum of the opposite angles is equal to 180 degrees.

What does the tangent-secant theorem state?

If a tangent and a secant are drawn from a point outside the circle, the square of the length of the tangent is equal to the product of the secant and its external segment.

What is the alternate segment theorem?

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

State the chord theorem.

Perpendicular from the center of a circle to a chord bisects the chord.

What is the inscribed angle theorem?

The inscribed angle is half the measure of the intercepted arc.

What does the angle in a semicircle theorem state?

An angle inscribed in a semicircle is a right angle.

What is the intersecting chords theorem?

If two chords intersect, the products of the lengths of the segments of each chord are equal.

State the power of a point theorem.

For a point outside a circle, the power of the point is the square of the length of the tangent segment drawn from the point minus the square of the radius of the circle.

What is the two tangents theorem?

If two tangents are drawn to a circle from an external point, they are equal in length.

What does the angle between the tangent and radius theorem state?

The angle between a radius and a tangent drawn at the point of contact is a right angle.

What is the arc length of a circle theorem?

The length of an arc is a fraction of the circumference of the circle, based on the angle subtended at the center.

What does the segment area theorem state?

The area of a segment of a circle can be calculated by subtracting the area of the corresponding triangle from the area of the sector.

What is the relationship between angles subtended by the same arc?

Angles subtended by the same arc at the circumference of a circle are equal.