Question

Теорема об отрезках пересекающихся хорд

Answer 1

Если две хорды окружности пересекаются, то произведение отрезков одной хорды равно произведению отрезков другой хорды

Answer 2

Если 2 хорды пересекаются то произведение отрезков одной хорды равно произведению отрезков другой хорды

Answer 3

Theorem of Intersecting Chords

The theorem of intersecting chords states that in a circle, the product of the lengths of the segments of two intersecting chords is equal. This theorem can be expressed as follows:

Theorem: In a circle, if two chords intersect, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

This theorem has various applications in geometry and can be used to solve problems related to intersecting chords in circles.

Application of the Theorem

The theorem of intersecting chords is often used to solve problems related to the lengths of segments formed by intersecting chords in a circle. It provides a fundamental relationship between the lengths of these segments, allowing for the calculation of unknown lengths based on the known lengths of other segments.

Mathematical Representation

The theorem of intersecting chords can be mathematically represented as follows:

Given a circle with two intersecting chords AB and CD, where the segments formed are AE, EB, CF, and FD, the theorem can be expressed as:

AE * EB = CF * FD

This equation illustrates the fundamental relationship described by the theorem, where the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

Conclusion

The theorem of intersecting chords provides a valuable tool for solving geometric problems involving intersecting chords in circles. By understanding and applying this theorem, mathematicians and students can effectively analyze and solve problems related to the lengths of segments formed by intersecting chords.