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2008 Harvard-MIT Mathematics Tournament
30
30
Part of
2008 Harvard-MIT Mathematics Tournament
Problems
(1)
Triangle Side System
Source: HMMT 2008 Guts Problem 30
5/13/2008
Triangle
A
B
C
ABC
A
BC
obeys
A
B
=
2
A
C
AB = 2AC
A
B
=
2
A
C
and
∠
B
A
C
=
12
0
∘
.
\angle{BAC} = 120^{\circ}.
∠
B
A
C
=
12
0
∘
.
Points
P
P
P
and
Q
Q
Q
lie on segment
B
C
BC
BC
such that \begin{eqnarray*} AB^2 + BC \cdot CP = BC^2 \\ 3AC^2 + 2BC \cdot CQ = BC^2 \end{eqnarray*} Find
∠
P
A
Q
\angle{PAQ}
∠
P
A
Q
in degrees.
trigonometry