Intersecting Secant Theorem

INTERSECTING SECANTS THEOREM. The measure of an angle formed by two secants, a secant and a tangent, or two tangents intersecting in the exterior of a circle is equal to one-half the positive difference of the measures of the intercepted arcs. a 1 2 c-b Problem 1 Solution x 12 141 - 61 x 12 80

The intersecting secants theorem states that when two secants intersect at an exterior point, the product of the one whole secant segment and its external segment is equal to the product of the other whole secant segment and its external segment. This is also known as the secant theorem or the secant power theorem.

Learn the relation of line segments created by two intersecting secants and the associated circle in Euclidean geometry. See the equation, proof, and references for the intersecting secants theorem and related topics.

Intersecting Secants Theorem. When two secant lines intersect each other outside a circle, the products of their segments are equal. Note Each segment is measured from the outside point Try this In the figure below, drag the orange dots around to reposition the secant lines. You can see from the calculations that the two products are always

Intersecting Secants Theorem If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

What is the Intersecting Secant Theorem or Segments of Secants Theorem? If two secant segments are drawn to a circle from the same external point, the product of the length of one secant segment and its external part is equal to the product of the length of the other secant segment and its external part.

Intersecting Secant Theorem. Author Caribou Contests. Two secants intersect and each secant is split into two segments. One from the intersection point to the nearest point from the circle. The second from the intersection point to the further point on the circle. The product of these two segments is equal for both secants.

Learn how to use the intersecting secants theorem to find missing angles and arcs on, in, or outside circles. See 15 examples, video lesson, and practice problems with solutions.

Learn how to use the intersecting secants theorem to find the product of two lengths of a circle. See examples, diagrams and explanations with similar triangles and inscribed angles.

Segments from Secants. When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other. Two Secants Segments Theorem If two secants are drawn from a common point outside a circle and the segments are labeled as below, then 92aabccd92. Figure 9292PageIndex192