Secant of a Circle Theorem

Various theorem related to Secant of a Circle Theorem are added below,

I. Tangent Secant Theorem

Tangent-Secant Theorem states that when you draw a tangent segment and a secant segment from an external point to a circle, the square of the length of the tangent segment is equal to the product of the length of the secant segment and its outer portion.

In a formula: (AB)² = AC × AD

Learn, Tangent Secant Theorem

II. Intersecting Secants Theorem

The Intersecting Secants Theorem states that if two secant segments are drawn from a point outside a circle, then the product of the length of one secant segment and its outer portion is equal to the product of the length of the other secant segment and its outer portion.

In a formula: MN × MO = MP × MQ

This theorem is applicable when you have two intersecting secants, such as MO and MQ in the provided figure, and it establishes a relationship between the lengths of these secant segments and their external portions.

III. Secant and Angle Measures

When two secant lines intersect inside a circle, the measure of each angle formed is half the sum of the measures of the arcs intercepted by those secants. In simpler terms, if you have two secant lines like AD and BC intersecting inside the circle at point O, then the size of the angle AOB is equal to half the sum of the lengths of the arcs AB and CD.

m∠AOB = 1/2(AB + CD)

Whereas, when two secant lines intersect outside the circle, the measure of the angle formed by these lines is half the positive difference between the measures of the intercepted arcs. For instance, in the circle with intersecting secant lines AC and AE outside the circle at point A, the angle CAE is equal to half the positive difference between the lengths of the arcs CE and BD.

m∠CAE = 1/2(CE – BD)