MathDB
Problems
Contests
National and Regional Contests
Ukraine Contests
Random Geometry Problems from Ukrainian Contests
Old Kyiv MO Geometry
Kyiv City MO Seniors 2003+ geometry
2018.10.4
2018.10.4
Part of
Kyiv City MO Seniors 2003+ geometry
Problems
(1)
angle wanted, altitudes of 2 trianlges related (2018 Kyiv City MO 10.4 )
Source:
9/12/2020
In the acute-angled triangle
A
B
C
ABC
A
BC
, the altitudes
B
P
BP
BP
and
C
Q
CQ
CQ
were drawn, and the point
T
T
T
is the intersection point of the altitudes of
Δ
P
A
Q
\Delta PAQ
Δ
P
A
Q
. It turned out that
∠
C
T
B
=
90
∘
\angle CTB = 90 {} ^ \circ
∠
CTB
=
90
∘
. Find the measure of
∠
B
A
C
\angle BAC
∠
B
A
C
. (Mikhail Plotnikov)
geometry
angles
altitudes