Question

Suppose you are given a circle. Give a construction to find its centre.

Answer 1

Hint: Since, the circle is given so first mark three points on the circle and from the middle point join the first point and from the middle point join the third point. Then take the compass and Draw a perpendicular bisector for the chords. Then at which the perpendicular bisectors intersect that point will be the centre of the circle.

Complete step-by-step answer:
Step 1. Draw the circle $ {C_1} $ .
Step 2. First let us take three points $ P $ , $ Q $ and $ R $ on the circle.
Step 3. Second Join $ PR $ and $ RQ $ .
Step 4. It is known that any perpendicular bisector of the chord passes through the centre.
So, now let use construct perpendicular bisectors of $ PR $ and $ RQ $ .
Step 4. Third, take a compass. With the help of point $ P $ as the end and $ R $ as the pencil end of the compass, mark arc in both the sides above and below of the line $ PR $ .
Step 5. Fourth join the arcs which are drawn using the compass.

Step 6. The line which is joined is the perpendicular bisector of $ PR $ .
Step 7. Fifth take a compass. With the help of point $ R $ as the end and $ Q $ as the pencil end of the compass, mark arc in both the sides above and below of the line $ RQ $ .
Step 8. With the help of point $ R $ as the end and $ Q $ as the pencil end of the compass, mark arc in both the sides above and below of the line $ RQ $ .
Step 9. Join the arcs which are drawn using the compass.
Step 10. The line which is joined is the perpendicular bisector of $ RQ $ .
Step 11. The point at which the two perpendicular bisectors intersect is the center of the circle.

Step 12. Take that point as $ O $ .
Hence, the $ O $ is the centre of the circle $ {C_1} $ .

Note: The tangents also can be drawn using compass and scale. By taking one point in the circle and drawing a line from the center to the point find the perpendicular bisector and draw the line. That will be our tangent.