3. The centres of all the circles passing through two
fixed points lie on the perpendicular bisector of
the line joining these two points
4. The perpendicular bisectors of all chords of a circle
pass through the centre of the circle.
All circles sharing a common chord have their centres
on the perpendicular bisector of this chord.
5. •The perpendicular through the midpoint of a
chord passes through the centre of the circle.
The perpendicular from the centre of a circle to
a chord passes through the midpoint of the
chord
6. LENGTH OF A CHORD
Consider a circle with centre O and a chord AB, r
be the radius and d be the perpendicular distance
from the centre to the chord AB, then length of the
chord is 2(√r2-d2)
7. CIRCUMCIRCLE
The circle which passes through all the three vertices
of a triangle is known as the circumcircle.
The centre of the circumcircle is the circumcentre
and radius of the circumcircle is the circumradius.
