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

**Solution:**

Construction:

Step 1: Draw a circle with a convenient radius.

Step 2: Draw 2 chords AB and PQ of any length.

Step 3: With A as center and radii more than half the length of AB, draw two arcs on opposite sides of chord AB. With the same radius and with B as center, draw two arcs cutting the former arcs. Join the line. Now DE is the perpendicular bisector of AB.

Step 4: With P as center and radii more than half the length of PQ, draw two arcs on opposite sides of chord PQ. With the same radius and with Q as the center, draw two arcs cutting the former arcs. Join the line. Now LM is the perpendicular bisector of PQ.

Step 5: As the center of the circle should lie both on DE and LM, it is obvious that the intersection points of DE and LM is the center of circle. Mark the intersection points as O.

Step 6: O is the required center of the circle.

**☛ Check: **NCERT Solutions for Class 9 Maths Chapter 10

**Video Solution:**

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

Maths NCERT Solutions Class 9 Chapter 10 Exercise 10.3 Question 2

**Summary:**

If you are given a circle, then construction to find its center is given by constructing two perpendicular bisectors as mentioned in the steps.

**☛ Related Questions:**

- Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centers.
- Prove that if chords of congruent circles subtend equal angles at their centers, then the chords are equal.
- Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

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