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 \(AC\).

## Comments

Sort by:

TopNewesti 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, 1 month ago

Log in to reply

How did your paper go? – Siddharth G · 2 years, 1 month ago

Log in to reply

How did yours go? – Siddhartha Srivastava · 2 years, 1 month ago

Log in to reply

– Siddharth G · 2 years, 1 month 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.Log in to reply

– Surya Prakash · 2 years, 1 month ago

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

@Sreejato Bhattacharya @megh choksi – Surya Prakash · 2 years, 1 month ago

Log in to reply