3. Let ABC be a triangle, with an obtuse angle at A. Let Q be a point
• One complete solution will gain more credit than
(other than A, B or C) on the circumcircle of the triangle, on the same
several unfinished attempts. It is more important
side of chord BC as A, and let P be the other end of the diameter
to complete a small number of questions than to
through Q. Let V and W be the feet of the perpendiculars from Q onto
try all the problems.
CA and AB respectively. Prove that the triangles P BC and AW V
• Each question carries 10 marks. However, earlier
are similar. [Note: the circumcircle of the triangle ABC is the circle
questions tend to be easier. In general you are
which passes through the vertices A, B and C.]
advised to concentrate on these problems first.
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