**Math Labs with Activity – Centre of a Circle**

**OBJECTIVE**

To find the centre of a given circle

**Materials Required**

- A sheet of transparent paper
- A geometry box
- A bangle

**Theory**

We verified in Activity 19 that the line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. From this it can be deduced that the perpendicular bisector of a chord passes through the centre of the circle. Thus, the perpendicular bisectors of any two chords of a circle will intersect at the centre of the circle.

**Procedure**

**Step 1:** Place the bangle on the sheet of transparent paper. With the help of the bangle draw a circle.

**Step 2:** Take any three distinct points A, B and C on the circle. Join AB and BC. Then, AB and BC are two chords of the circle.

**Step 3:** Fold the paper along the line which cuts the chord AB in such a way that the point A lies exactly over the point B. Form a crease and unfold the paper. Draw a line PQ on this crease. Then, PQ is the perpendicular bisector of the chord AB.

**Step 4:** Again fold the paper along the line which cuts the chord BC in such a way that the point B lies exactly over the point C. Form a crease and unfold the paper. Draw a line MN on this crease.

Then, MN is the required perpendicular bisector of the chord BC (see Figure 21.1).

**Observations**

We observe that the lines PQ and MN intersect at a point O inside the circle.

**Result**

The point of intersection, O, of the perpendicular bisectors of the two chords of the circle is the centre of the given circle.

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