Question 81
In an isosceles triangle $ABC$ with $AC = BC \neq AB$, fix a point $P$ on the base $AB$. How many positions can a point $Q$ in the plane take if we want the points $A, P$ and $Q$, taken in any order, to be the vertices of a triangle similar to $ABC$?
(A) 0
(B) 2
(C) 3
(D) 4
(E) 6.
(A) 0
(B) 2
(C) 3
(D) 4
(E) 6.