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It is a Descriptive geometry problem, the solution of which will allow to correctly, graphically draw the reflection of sound (architectural acoustic calculation) from an unknown point on a given circular surface (this is the point that needs to be found) coming from a given point A to a given point B.

Taking into account the laws of reflection of sound (laws: For any surface, the angle between the incident sound ray and that surface is equal to the angle between the reflected ray and that surface.) Let's formulate the problem like this:

Given a circle with center O and two points inside that circle, A and B, it is required to construct the polygonal chain (line segments) ACB that intersects the given circle at point C, and the angle formed by the segment AC and the tangent drawn to the circle at point C must be equal to the angle formed by the segment CB and the tangent drawn at point C. Under these conditions, the polygonal chain (line segments) ACB will be the shortest of all possible polygonal chains (line segments) that start at point A, intersect the circle, and end at point B. The solution must be such that it will be possible to construct (graphically draw) the unknown point C, using the given knowns

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Vahagn Ayvazyan
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    Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be closed. To prevent that, please [edit] the question. This will help you recognize and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Nov 23 '24 at 11:12
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    This is Alhazen's problem. It can be solved in several ways, see for instance this old answer of mine. In general, it leads to a quartic equation and the construction cannot be made with ruler and compass. – Intelligenti pauca Nov 23 '24 at 11:59
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    @JoséCarlosSantos thanks for the comment. I am an architect, a student, I study many different fields, I am engaged in self-education. This question arose for me while studying architectural acoustics, so I decided to create this question. This was my first question, next time I will try to make the question more contextual. – Vahagn Ayvazyan Nov 23 '24 at 12:46
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    @Intelligenti pauca Thank you for the reply and for clarifying me of the name of the problem. I will try to study it thoroughly. – Vahagn Ayvazyan Nov 23 '24 at 12:49

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