self Maths Puzzle

Triangle ABC acute triangle.
H is orthocentre,
BC is diameter.
AM & AN are tangents
prove that M, H. & N are collinear.

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self Other Question

" ABC
*ABC
-------
---ABC

where C is odd, but not 5.
What is the last three digit of 78^2365 and 67^2365
without using binomial theorem?