# RMO 2014 Delhi Region Q.5

Let $ABC$ be an acute-angeled triangle and let $H$ be its orthocenter. For any point $P$ on the circumcircle of triangle $ABC$, let $Q$ be the point of the intersection of the line $BH$ with the line $AP$ . Show that there is a unique point $X$ on the circumcircle of $ABC$ such that for every point $P\not=A,B$ the circumcircle of $HQP$ pass through $X$.

• You can find rest of the problems here

• You can find the solutions here Note by Aneesh Kundu
4 years, 11 months ago

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I got this! I hope it is right.

- 4 years, 11 months ago

How?

- 4 years, 11 months ago

Take any other point say, $Z$ and let $AZ$ intersect $BH$ at $Y$. And consider circle $HYZ$ meeting circle $ABC$ at $X.$ Now,prove $HQPX$ is a cyclic quad!

- 4 years, 11 months ago

How many are you getting right? (Outta 6, right?)

- 4 years, 11 months ago

I solved 4

- 4 years, 11 months ago

Dunno whether they are right or wrong

- 4 years, 11 months ago

can someone give me the solution to this problem? plzz

- 4 years, 11 months ago

Quite similar to one which came in Rajasthan paper, though more difficult.

- 4 years, 11 months ago