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Ireland National Math Olympiad
2015 Irish Math Olympiad
8
8
Part of
2015 Irish Math Olympiad
Problems
(1)
if |DE| =|BC|, find angle <BAC, perpendicular - circumcircle
Source: Irmo 2015 p2 q8
9/16/2018
In triangle
△
A
B
C
\triangle ABC
△
A
BC
, the angle
∠
B
A
C
\angle BAC
∠
B
A
C
is less than
9
0
o
90^o
9
0
o
. The perpendiculars from
C
C
C
on
A
B
AB
A
B
and from
B
B
B
on
A
C
AC
A
C
intersect the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
again at
D
D
D
and
E
E
E
respectively. If
∣
D
E
∣
=
∣
B
C
∣
|DE| =|BC|
∣
D
E
∣
=
∣
BC
∣
, find the measure of the angle
∠
B
A
C
\angle BAC
∠
B
A
C
.
geometry
perpendicular
circumcircle