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National and Regional Contests
Italy Contests
ITAMO
1995 ITAMO
4
4
Part of
1995 ITAMO
Problems
(1)
equal segments wanted, circumcircle and angle bisector related
Source: 1995 ITAMO p4
1/28/2020
An acute-angled triangle
A
B
C
ABC
A
BC
is inscribed in a circle with center
O
O
O
. The bisector of
∠
A
\angle A
∠
A
meets
B
C
BC
BC
at
D
D
D
, and the perpendicular to
A
O
AO
A
O
through
D
D
D
meets the segment
A
C
AC
A
C
in a point
P
P
P
. Show that
A
B
=
A
P
AB = AP
A
B
=
A
P
.
geometry
circumcircle
equal segments
angle bisector