# INMO 2015 PROB 1

Let $$\Delta ABC$$ be a right angled triangle with $$\angle B = 90^{0}$$. Let $$BD$$ be altitude from $$B$$ on to $$AC$$. Let $$P,Q$$ and $$I$$ be incenters of triangles $$\Delta ABD, \Delta CBD$$ and $$\Delta ABC$$ respectively. Show that the circumcenter of triangle $$\Delta PIQ$$ lies on the hypotenuse $$AC$$.

Note by Surya Prakash
3 years, 4 months ago

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i solved this question by using coordinate geometry, taking B as the origin. This year paper was a bit easier than last year except problem 5

- 3 years, 4 months ago

- 3 years, 4 months ago

I solved 2, messed up the functional equation >.<. And my proof for Q2 had quite a bit of hand waving, so can't really expect full marks for it.

How did yours go?

- 3 years, 4 months ago

Confident on the 4th, Ok with the 2nd and 6th(?), bashed up the third. How did you answer the sixth? My answer concluded that even 9 integers would suffice, found a problem with that.

- 3 years, 4 months ago

confident with 4th and 6th.... but a bit wrong with final computation in Q4.

- 3 years, 4 months ago