Question

Give a construction to find the centre of the circle.

Give Explanation with diagram...​

Answer 1

★ Steps of construction :

(a) Take any three points A, B and C on the circle.

(b) Join AB and BC.

(c) Draw perpendicular say LM of AB.

(d) Draw perpendicular PQ of BC.

(e) Let LM and PQ intersect at point O.

Then O is the centre of the circle.

★ Verification :

O lies on the perpendicular of AB.

OA = OB ……….(i)

O lies on the perpendicular of BC.

OB = OC ……….(ii)

From eq. (i) and (ii), we observe that

OA = OB = OC = (say)

Three non-collinear points A, B and C are at equal distance (r) from the point O inside the circle.

Hence, O is the centre of the circle.

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Answer 2

Answer:

Draw a line across the circle to make a "chord"

Construct the perpendicular bisector of that chord to make a diameter of the circle.

Construct the perpendicular bisector of that diameter to get the center of the circle.

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