LET ABC BE A TRIANGLE, WITH AN OBTUSE ANGLE AT A. LET Q BE A POINT•...

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.