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PS-1

In this task, we can think of B and C as fixed, along with the angle at B.
As point A moves to the right, the angle at A gets smaller so the slope of the bisector of angle A gets closer to the horizontal, ie the line 'dips down'. This might suggest that as A moves to the right, P moves downwards. However, it turns out that this is not the case.

One way to look at this task is to consider the bisector of angle C and where, in particular, it meets the bisector of angle B. What happens to this point as A moves to the right and angle C gets bigger?

Another approach is to use the fact that the circle which touches all three sides of triangle ABC has its centre at P. (Why?) As A moves to the right, there is more room for the circle to grow upwards and to the right - what happens to its centre? Where is the centre when A is 'at infinity'?

We show a related task on the next page: PS-2

FREE:
a high-res pdf file of this new GEOaa-zz task