Mathematics
Class-X
2015-2016
Example – 1 : In the given figure,
are two isosceles triangle on the same base
BC. Show that the line PQ when produced bisects BC and is perpendicular to BC.
Solution : - Let PQ when produced meet BC at M.
And QB = QC Q is equidistant from B and C
Q lies on the perpendicular bisector of BC.
is the perpendicular bisector of BC.
Hence PQM bisector BC and is perpendicular to BC.
Example – 2 : In the adjoining figure, the bisector of
intersect at a point P.
Show that P is a equidistant from the opposite sides BA and CD.
of a quadrilateral ABCD
Solution : Let PM and PN be perpendicular to AB and CD respectively. PL is drawn
perpendicular to BC.
P lies on the bisector of
Again P leis on the bisector of
From (i) and (ii) we get
PM = PN
Hence, P is equidistant from BA and CD.
Sudheer Gupta .
Be positive and constructive. 
Page 1
Mathematics
Class-X
2015-2016
Example - 3 : A and B are two fixed points in a plane. Find the locus of a point P which moves
in such a way that PA2 + PB2 = AB2.
Solution : PA2 + PB2 = AB2 is true only when
Also, angle in a semi-circle is a right angle.
So, we draw a circle with AB as a diameter and take any point P on the cirlcle.
Hence, the locus of P is the circumference of a circle with AB as a diameter.
Sudheer Gupta .
Be positive and constructive. 
Page 2