RMO 2014 Delhi Region Q.5

Let ABCABC be an acute-angeled triangle and let HH be its orthocenter. For any point PP on the circumcircle of triangle ABCABC, let QQ be the point of the intersection of the line BHBH with the line APAP . Show that there is a unique point XX on the circumcircle of ABCABC such that for every point PA,BP\not=A,B the circumcircle of HQPHQP pass through XX.


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Note by Aneesh Kundu
4 years, 8 months ago

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I got this! I hope it is right.

Ranjana Kasangeri - 4 years, 8 months ago

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How?

Aneesh Kundu - 4 years, 8 months ago

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Take any other point say, ZZ and let AZAZ intersect BHBH at YY. And consider circle HYZHYZ meeting circle ABCABC at X.X. Now,prove HQPXHQPX is a cyclic quad!

Ranjana Kasangeri - 4 years, 8 months ago

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

Satvik Golechha - 4 years, 8 months ago

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I solved 4

Aneesh Kundu - 4 years, 8 months ago

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Dunno whether they are right or wrong

Aneesh Kundu - 4 years, 8 months ago

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can someone give me the solution to this problem? plzz

Nihar Mahajan - 4 years, 8 months ago

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

Satvik Golechha - 4 years, 8 months ago

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