Draw a circle with centre at a point O and radius 5.6 cm. Draw any chord AB. Draw a perpendicular bisector of AB. Does the bisector pass through the centre O ?

Answer

### Step-by-Step Solution:

1. **Draw the Circle:**
- Start by marking a point on your paper and label it as point O. This will be the center of your circle.
- Using a compass, set the radius to 5.6 cm. Place the pointed end of the compass on point O and draw a circle.

**Hint:** Make sure the compass is adjusted to exactly 5.6 cm to ensure the circle is drawn accurately.

2. **Draw a Chord AB:**
- Choose any two points on the circumference of the circle and label them as A and B. Connect these points with a straight line to form chord AB.

**Hint:** The chord should be straight and should not exceed the diameter of the circle.

3. **Find the Perpendicular Bisector of AB:**
- With the compass, measure more than half the length of chord AB. Place the compass pointer on point A and draw an arc above and below the line segment AB.
- Without changing the compass width, place the compass pointer on point B and draw two arcs that intersect the previous arcs above and below the line segment AB.

**Hint:** Ensure the compass width is more than half of AB to create intersecting arcs.

4. **Mark the Points of Intersection:**
- Label the points where the arcs intersect as A' and B'.

**Hint:** These points should be clearly marked as they will help in drawing the perpendicular bisector.

5. **Draw the Perpendicular Bisector:**
- Use a ruler to draw a straight line connecting points A' and B'. This line is the perpendicular bisector of chord AB.

**Hint:** The perpendicular bisector should intersect chord AB at its midpoint.

6. **Check if the Bisector Passes Through the Center O:**
- Observe the drawn perpendicular bisector. If it intersects point O, then it passes through the center of the circle.

**Hint:** The perpendicular bisector of any chord in a circle always passes through the center of the circle.

### Conclusion:
Yes, the perpendicular bisector of chord AB does pass through the center O of the circle.