Congruent chords are equidistant from the centre of a circle

In the same circle or in circles of equal radius:

• Equal chords are equidistant from the centre.

• Conversely, chords that are equidistant from the centre are equal.

Objectives
Understanding equal chords are at equal distance from the centre

Estimated Time
40 minutes

Prerequisites/Instructions, prior preparations, if any
Basics of circles and its related terms should have been done.

Materials/ Resources needed
This geogebra file has been created by Tharanath Achar of Dakshina kannada.
 * Digital : Computer, geogebra	application, projector.
 * Non	digital : Worksheet	and pencil, compass, strings
 * Geogebra	files : Equal	chords and distance from center.ggb, Equidistantchords.ggb

Process (How to do the activity)
Developmental Questions Equal chords and distance from center.ggb Equidistantchords.ggb
 * 1) What is a chord ?
 * 2) Name the centre of the circle.
 * 3) How do you draw congruent chords in a circle ?
 * 4) How many chords do you see in the figure ? Name them.
 * 5) If  both the chords are congruent, what can you say about the length of both the chords ?
 * 6) How can we measure the length of the chord ?
 * 7) What is the procedure to draw perpendicular bisector ?
 * 8) What does theorem 1 say ? Do you all remember ?
 * 9) What is the length of both chords here ?
 * 10) What can you conclude ?
 * 11) Repeat this for circles of different radii and for different lengths of congruent chords.
 * 1) Two	chords equal chords are at equal angles with diameter from	a point on the circle.
 * 2) Identify the congruent elements for the triangles formed when	perpendicular is drawn to chords from center of the circle.
 * 3) Can these equal chords be any where in the circle, then what about	their perpendicular distances.
 * 1) Use the files to demonstrate equal chords are at equal distance from	the center
 * 2) Show the animation by overlapping the two chords to show they are	equal
 * Evaluation Questions
 * 1) Were the students able to comprehend the drawing of congruent chords in a circle ?
 * 2) Were the students able to comprehend why congruent chords are always equal for a given circle. Let any student explain the analogy.
 * 3) Are the students able to understand that this theorem can be very useful in solving problems related to circles and triangles ?
 * 4) What is a chord ?
 * 5) What are congruent chords ?
 * 6) Why do you think congruent chords are always equal for a circle of given radius ?