Let Φ be the hyperbola xy = b², b ≠ 0, and
P be a point on Φ.
Let Q be the image of reflection of P about
the origin. Construct a circle ω centred at P
with radius PQ.
ω cuts Φ at the points B, C, D, Q.
Prove that ΔBCD is equilateral, no matter
what the value of b is.
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