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Triangle Theorems
Hard
Triangle vertices angles and line intersection
Consider a triangle
ABC
having the vertices
A
(
1
,
2
)
,
B
(
α
,
β
)
and
C
(
γ
,
δ
)
and angles
∠
ABC
=
π
6
and
∠
BAC
=
2
π
3
. If the points
B
and
C
lie on the line
y
=
x
+
4
, then
α
2
+
γ
2
is equal to
.
.
.
.
.
.
.
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