Chord to Arc Relationships, Perpendicular Chord to Diameter, and Equidistant Chords to Center of Circle.

Did you know why a perpendicular diameter to a chord bisects both the chord, and the arc intercepted by the chord? Are you aware that the distance to the center of two congruent chords in the same circle, or in circles that are congruent is the same for both?

This is a very good lesson that makes an emphasis in teaching how to solve problems that involve these theorems. It is a short lesson, but it will be of great value to you!

Lesson's Content

Lesson's Glossary

Arc
The curved segment that is between two points in the circumference of a circle.

Arc length
The distance between an arc's endpoints along the path of the circle.

Center of a circle
The point that all points in the circle are equidistant from.

Central angle of a circle
An angle whose vertex is the center of the circle.

Chord of a circle
A segment whose endpoints are on a circle.

Circle
The set of points on a plane at a certain distance (radius) from a certain point (center); a polygon with infinite sides

Radii
Plural form of radius.

Radius
The segment whose endpoints are any point on a circle or sphere and its center; the length of that segment.

Interactive Geometric Applets: Relevant Theorems.

If you have a diameter perpendicular to the chord, then this cuts in half to

both the chord, and its intercepted arc. This theorem may be verified

by dragging up and down point "B". Pay special attention on how

the chord and the arc update their bisected values.

Given two congruent chords in the same circle or in congruent circles the intercepted arcs

are congruent as well. This is also true for the converse of the theorem. Interact with this

geometric applet to verify it.

Two congruent chords in congruent circles or in the same circle are equidistant from the

center of the circle; the converse of the theorem is also true.

Play with this interactive geometric applet to visualize it in a dynamic way.

Didn't you find what you were looking for? Do your search here!