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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 \(X\).
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Aneesh Kundu
2 years, 10 months ago
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Top NewestQuite similar to one which came in Rajasthan paper, though more difficult.
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can someone give me the solution to this problem? plzz
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How many are you getting right? (Outta 6, right?)
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Dunno whether they are right or wrong
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I solved 4
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I got this! I hope it is right.
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How?
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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!
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