Question

Theorem
find the centre and radius.
Taking the centre and the radius so obtained, we
can complete the circle (see Fig. 9.20).
Fig. 9.20
EXERCISE 9.3
1. Draw different pairs of circles. How many points does each pair have in common?
What is the maximum number of common points?
2. Suppose you are given a circle. Give a construction to find its centre.
3. If two circles intersect at two points, prove that their centres lie on the perpendicular
bisector of the common chord.
191​

Answer 1

Solution−

Wedrawpairsofcirclessothat

(i)Thedistancebetweenthecentres>thesumoftheirradii,

(ii)Thedistancebetweenthecentres=thesumoftheirradii,

(ii)Thedistancebetweenthecentres<thesumoftheirradii,

(ii)Thedistancebetweenthecentres=0

Take(a)differetradii(b)equalradii.

InfigI

Thedistancebetweenthecentres>thesumoftheirradii,

⟶Nocommonpoint.

InfigII

Thedistancebetweenthecentres=thesumoftheirradii,

⟶Onecommonpoint.

InfigIII

Thedistancebetweenthecentres<thesumoftheirradii,

⟶Twocommonpoints.

InfigIVa

Thedistancebetweenthecentres=0andtheradiiaredifferent.

⟶Nocommonpoint.

InfigIVb

Thedistancebetweenthecentres=0andradiiareequal.

Thecircleswillcoincide.

⟶Infinitenumberofcommonpoints.

Ans−OptionC,