MathDB
Problems
Contests
National and Regional Contests
Pakistan Contests
Pakistan TST
2017 Pakistan TST
Problem 1
Problem 1
Part of
2017 Pakistan TST
Problems
(1)
Perpendicularity in Cyclic Quad.
Source: Pakistan TST(2) 2017.P1
1/28/2017
Let
A
B
C
D
ABCD
A
BC
D
be a cyclic quadrilateral. The diagonals
A
C
AC
A
C
and
B
D
BD
B
D
meet at
P
P
P
, and
D
A
DA
D
A
and
C
B
CB
CB
meet at
Q
Q
Q
. Suppose
P
Q
PQ
PQ
is perpendicular to
A
C
AC
A
C
. Let
E
E
E
be the midpoint of
A
B
AB
A
B
. Prove that
P
E
PE
PE
is perpendicular to
B
C
BC
BC
.
cyclic quadrilateral
perpendicular lines
geometry