**Math Labs with Activity – Equal Chords of a Circle are Equidistant**

**OBJECTIVE**

To verify that equal chords of a circle are equidistant from the centre of the circle

**Materials Required**

- A sheet of transparent paper
- A geometry box

**Theory**

The length of the perpendicular drawn from the centre of a circle to a chord gives the distance of the chord from the centre of the circle.

**Procedure**

**Step 1:** Mark a point O on the sheet of transparent paper.

With O as the centre, draw a circle of any radius.

**Step 2:** Draw two equal chords AB and PQ in this circle. (Adopt the procedure discussed in Activity 15.)

**Step 3:** Fold the paper along the line which passes through O and cuts the chord AB such that one part of the chord AB overlaps the other part.

Make a crease and unfold the paper. Mark the point M where the line of fold cuts the chord AB. Join OM. Then, OM ⊥ AB. Thus, OM is the distance of the chord AB from the centre O of the circle.

**Step 4:** Again fold the paper along the line which passes through O and cuts the chord PQ such that one part of the chord PQ overlaps the other part.

Make a crease and unfold the paper. Mark the point N where the line of fold cuts the chord PQ. Join ON. Then, ON ⊥ PQ. Thus, ON is the distance of chord PQ from the centre O of the circle.

**Step 5:** Fold the paper along the line passing through the centre O of the circle such that the line OM overlaps the line ON.

**Observations**

When the paper is folded along the line passing through O such that the line OM overlaps the line ON, we observe that the point M lies exactly over the point N.

Therefore, OM =ON, i.e., the distance of the chord AB from O = the distance of the chord PQ from O.

**Result**

It is verified that equal chords of a circle are equidistant from the centre of the circle.

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