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

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Center of the circle

The perpendicular bisectors of any two chords will never meet

Both 1 and 2

None of the above

answer is A.

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Detailed Solution

Take a 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.
seo

AB and CD are two random chords in the given circle.
Now we need to construct perpendicular bisectors to both chords AB and CD.
For that, follow the following steps:
Step 1. By using a compass, take a distance more than half of CD and draw an arc to both the sides of the chord CD, by taking C as center.
Step 2. Now, without changing the distance that you took while drawing arcs from C as center, 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. Now join PQ using a ruler.
Step 4. Let us repeat the same 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
seo

From the diagram we can see that the perpendicular bisectors of any two chords of a circle intersect at the center of the circle.
So, option (1) is correct for this question.

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