Question

theorem of external division of chords​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Theorem of external division of chords states that if a line is drawn through a circle intersecting two distinct points of the circle, then the product of the line segments created by the points of intersection is equal.

Here are some key points to keep in mind regarding the theorem of external division of chords:

• In other words, let P and Q be two distinct points on a circle with center O, and let the line through P and Q intersect the circle at points A and B respectively. Then, the product of the lengths of PA and AQ is equal to the product of the lengths of PB and BQ, i.e., PA x AQ = PB x BQ.
• This theorem is a specific case of the more general power of a point theorem, which relates the lengths of line segments from a point outside a circle to the circle itself.
• The theorem of external division of chords can be used to solve problems involving tangents to circles, chords intersecting inside or outside a circle, and many other geometrical constructions involving circles.
• The theorem can also be extended to apply to more than two points of intersection with the circle, where the product of the segments formed by each point of intersection is equal.
• The theorem has many practical applications in fields such as engineering, architecture, and physics, where circles and spheres are commonly used in constructions and calculations.
• Overall, the theorem of external division of chords is a fundamental result in geometry and has many important applications in various fields of study.

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