MathDB
Problems
Contests
National and Regional Contests
India Contests
ISI B.Math Entrance Exam
2005 ISI B.Math Entrance Exam
3
3
Part of
2005 ISI B.Math Entrance Exam
Problems
(1)
B.Math - quadrilateral
Source:
6/20/2012
Let
A
B
C
D
ABCD
A
BC
D
be a quadrilateral such that the sum of a pair of opposite sides equals the sum of other pair of opposite sides
(
A
B
+
C
D
=
A
D
+
B
C
)
(AB+CD=AD+BC)
(
A
B
+
C
D
=
A
D
+
BC
)
. Prove that the circles inscribed in triangles
A
B
C
ABC
A
BC
and
A
C
D
ACD
A
C
D
are tangent to each other.
geometry