triangle: altitudes of scalene, sharp-angled triangle ABC intersect in point H

kamilox55

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this problem is contest problem
 

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clearly there's a picture for this material, so include the picture for it.

the altitudes intersect at point H, namely H is the orthocenter, but there's a circumscribing circle, so we need to see the whole thing.
 
Hello i'm new in this forum and i want to get our help, please.

The altitudes of the scalene, sharp-angled triangle ABC intersect
in point H. The point S is the center of the arc BC of the circle described in
the BCH triangle, which contains the H point. Determine the angle measure BAC if
the equality AH = AS is met.

I'm know that i'm bad in english, but i'm hope that you were understood my question.

The one word I'm having trouble with is "described". I think you mean "circumscribed about", since this circle seems to pass through points B, C, and H. But I can't see how to make AH = AS without making an angle of ABC obtuse.

Ah! Now I see that I was taking S to be the center of the circle; I think you mean it to be the midpoint of the arc BC.

For your information, here is my rewording of your question in slightly clearer English, as I understand it:


The altitudes of the scalene, acute-angled triangle ABC intersect in point H. The point S is the midpoint of the arc BC of the circle circumscribed about triangle BCH, which contains the point H. Determine the measure of angle BAC if the equality AH = AS is satisfied.

I have experimented with a drawing in GeoGebra, and don't see a consistent answer, so I may still be misunderstanding the problem.

Now we need one thing more: Please tell us what you have tried, and where you need help. We can't really tell how you should approach the problem, without having any idea of what you have learned that might be of use, or whether the problem came from a class or, say, a contest.

If you haven't yet read our guidelines, please do, in order to understand what is needed.
 
I don't do English math tasks every day, but the forum in my country doesn't help. This is math contest and the level of this competition is at the high school level.
 
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