# Congruent chords are equidistant from the centre of a circle

From Karnataka Open Educational Resources

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

- Digital : Computer, geogebra application, projector.
- Non digital : Worksheet and pencil, compass, strings
- Geogebra files : Equal chords and distance from center.ggb, Equidistantchords.ggb

This geogebra file has been created by Tharanath Achar of Dakshina kannada.

Download this geogebra file from this link.

Download this geogebra file from this link.

### Process (How to do the activity)

Developmental Questions

- What is a chord ?
- Name the centre of the circle.
- How do you draw congruent chords in a circle ?
- How many chords do you see in the figure ? Name them.
- If both the chords are congruent, what can you say about the length of both the chords ?
- How can we measure the length of the chord ?
- What is the procedure to draw perpendicular bisector ?
- What does theorem 1 say ? Do you all remember ?
- What is the length of both chords here ?
- What can you conclude ?
- Repeat this for circles of different radii and for different lengths of congruent chords.

Equal chords and distance from center.ggb

- Two chords equal chords are at equal angles with diameter from a point on the circle.
- Identify the congruent elements for the triangles formed when perpendicular is drawn to chords from center of the circle.
- Can these equal chords be any where in the circle, then what about their perpendicular distances.

Equidistantchords.ggb

- Use the files to demonstrate equal chords are at equal distance from the center
- Show the animation by overlapping the two chords to show they are equal

**Evaluation Questions**

- Were the students able to comprehend the drawing of congruent chords in a circle ?
- Were the students able to comprehend why congruent chords are always equal for a given circle. Let any student explain the analogy.
- Are the students able to understand that this theorem can be very useful in solving problems related to circles and triangles ?
- What is a chord ?
- What are congruent chords ?
- Why do you think congruent chords are always equal for a circle of given radius ?