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 $AC$ .

#Geometry #INMO

Easy Math Editor

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Comments

@Sreejato Bhattacharya @megh choksi

Surya Prakash - 6 years, 4 months ago

How did your paper go?

Siddharth G - 6 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?

Siddhartha Srivastava - 6 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.

Siddharth G - 6 years, 4 months ago

@Siddharth G – confident with 4th and 6th.... but a bit wrong with final computation in Q4.

Surya Prakash - 6 years, 4 months ago

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

Kislay Raj - 6 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$