What is two intersecting chord theorem?

The intersecting chords theorem or just the chord theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.

When two chords intersect each other inside a circle the products of their segments are equal proof?

The intersecting chords theorem states that when two chords intersect at a point, P, the product of their respective partial segments is equal.

How does intersecting chords work?

When two chords intersect each other inside a circle, the products of their segments are equal. One chord is cut into two line segments A and B. The other into the segments C and D. This theorem states that A×B is always equal to C×D no matter where the chords are.

Which is the proof of the intersecting chords theorem?

AP/CP = BP/DP = AB/CD. The first identity (AP/CP = BP/DP) leads directly to the Intersecting Chords Theorem: AP·DP = BP·CP. Since the proof only uses the equality of the first two ratios, a keen observer might inquire whether the third ratio (AB/CD) is of any use.

What happens when two chords intersect in a circle?

Intersecting Chords Theorem. If two chords intersect inside a circle then the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.

How are the product of segments of intersecting chords equal?

Products of segments of intersecting chords are equal. If two chords intersect inside a circle then the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.

How to prove the intersecting secants theorem in geometry?

In today’s lesson, we will present a detailed, step-by-step proof of the Intersecting Secants Theorem, using properties of similar triangles. This is a fairly simple proof, so today’s lesson will be short.