If a number of circles pass through the end points P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ. Write ‘True’ or ‘False’ and justify your answer

Solution:

Draw a line segment PQ and S1 S2 S3 …. Sn are n circles with center C1 C2 C3 … Cn passing through P and Q

Sp PQ will be a chord to a circle or the diameter (It is possible once when diameter length is equal to the length of PQ)

If PQ is diameter then the center lies on the half of diameter i.e. on the perpendicular bisector of PQ.

If PQ is a chord then perpendicular from the center to the chord of circle bisect the chord

It implies that the center lies on the perpendicular bisector of the chord.

For each circle the center lies on the perpendicular bisector of PQ.

Therefore, the statement is true.

✦ Try This: In the following figure, the line ABCD is perpendicular to PQ where P and Q are the centres of the circle show that: (i) AB = CD

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10

NCERT Exemplar Class 10 Maths Exercise 9.2 Problem 9

If a number of circles pass through the end points P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ. Write ‘True’ or ‘False’ and justify your answer

Summary:

The statement “If a number of circles pass through the end points P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ” is true

☛ Related Questions:

• AB is a diameter of a circle and AC is its chord such that ∠BAC = 30°. If the tangent at C intersect . . . .
• If d₁, d₂ (d₂ > d₁) be the diameters of two concentric circles and c be the length of a chord of a c . . . .
• If a, b, c are the sides of a right triangle where c is the hypotenuse, prove that the radius r of t . . . .