Let $A_1, B_1, C_1$ be three points in the xy-plane. Suppose that the lines $A_1 C_1$ and $B_1 C_1$ are tangents to the curve $y^2=8 x$ at $A_1$ and $B_1$, respectively. If $O=(0,0)$ and $C_1=(-4,0)$, then which of the following statements is (are) TRUE?
Select ALL correct options:
A
The length of the line segment $O 4_1$ is $4 \sqrt{3}$
B
The length of the line segment $A_1 B_1$ is 16
C
The orthocentre of the triangle $A_1 B_1 C_1$ is $(0,0)$
D
The orthocentre of the triangle $A_1 B_1 C_1$ is $(1,0)$
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