Question

Draw a circle of radius $ 4cm $ . Draw any two of its chords. Construct the perpendicular bisector of these two chords. Where do they meet?

Answer 1

Hint: Chord is a line that is drawn inside a circle such that it intersects the circle at any two points. We can draw a perpendicular bisector to any line using steps of construction. Perpendicular bisector is a perpendicular line that divides the given line in two equal parts.

Complete step-by-step answer:
Consider any point O on the paper.
Taking this point O as a center. Draw a circle of radius $ 4cm $ .
Then use a ruler to draw any two straight lines inside the circle such that they intersect the circle at two points.
Name them, AB and CD.
Refer to the following figure.

AB and CD are any two random chords in the circle with center O.
Now we have to construct perpendicular bisectors to both AB and CD.
For that, follow the following steps:
Step 1. Using compass, considering C as center, take a distance more than half of CD and draw an arc to both the sides of the chord CD.
Step 2. Now, without changing the distance that you considered while drawing arcs from C as center, put your compass on D. Then, taking D as center, draw two arcs to both the sides of the chord CD at the same distance, such that, the arcs intersect the arcs drawn from C.
Step 3. Let us say that the arcs intersect at P and Q. Now join PQ using a ruler.
Step 4. Repeat the same construction for the chord AB. Let us say that the arcs drawn intersect at points X and Y. join XY using a ruler.
Step 5. Extend the lines PQ and XY until they intersect.
After all these steps, you will have a diagram that will look similar to this diagram

From the diagram you have drawn and the diagram you can observe here. You can see that the perpendicular bisectors of any two chords of a circle intersect at the center of the circle.

Note: While constructing a perpendicular bisector to any line. You should always take the distance to be more than half of the length of the line to draw arcs. Otherwise, the arcs you draw will never intersect. And you cannot have a perpendicular line if you don’t have points to join.