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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
2 years, 5 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 Kislay Raj · 2 years, 5 months ago

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How did your paper go? Siddharth G · 2 years, 5 months ago

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@Siddharth G 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 · 2 years, 5 months ago

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@Siddhartha Srivastava 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 · 2 years, 5 months ago

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@Siddharth G confident with 4th and 6th.... but a bit wrong with final computation in Q4. Surya Prakash · 2 years, 5 months ago

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@Sreejato Bhattacharya @megh choksi Surya Prakash · 2 years, 5 months ago

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