**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.

Math Labs with ActivityMath LabsScience Practical SkillsScience Labs

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