Circle Theorem: Arcs and Chords

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High School Math based on the topics required for the Regents Exam conducted by NYSED.

Circle Theorems for Arcs and Chords:

  1. If two chords are congruent, then their corresponding arcs are congruent.
  2. If the diameter or radius is perpendicular to a chord, then it bisects the chord and its arc.
  3. In the same circle or congruent circles, two chords are congruent if and only if they are equidistant from the center.

The following figures give the circle theorems for chords and perpendicular bisector. Scroll down the page for more examples and solutions.
Circle Theorems

Arcs and Chords
This video will demonstrate the above three theorems and how they may be used.

Circle Geometry
Using Chords Equidistant From the Center This geometry video math lesson deals with circle geometry. The main focus of this video is using the Chords Equidistant from the Center of a Circle Theorem. The theorem states: chords equidistant from the center of a circle are congruent and congruent chords are equidistant from the center of a circle.

Chords and Arcs
This lesson takes a look at chords and arcs and the theorems associated with them and the circles that they are a part of. Few examples are worked out.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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