072. Tri-Angle

Codeforces

IDCF10269072

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Given the three points that represent the corners of an isosceles triangle, determine the angle that the triangle is pointing. The angle can be calculated based on the vector created along the line of symmetry of the triangle that exits through the point of the triangle. The angle should be represented in degrees and should be determined relative to the vector (1,0). The following image shows a triangle with points at (-1,0), (0,1), and (-2,2), and has an angle of 135 degrees. Each line contains two space-separated floating point values that represent the $x$ and $y$ values of each point of the triangle. They are randomly ordered. A single floating point value that represents the degree measure of the angle created from the positive x-axis to the direction of the triangle. Make sure answers are provided in degrees and fall within the range of 0 to 360. ## Input Each line contains two space-separated floating point values that represent the $x$ and $y$ values of each point of the triangle. They are randomly ordered. ## Output A single floating point value that represents the degree measure of the angle created from the positive x-axis to the direction of the triangle. [samples] ## Note Make sure answers are provided in degrees and fall within the range of 0 to 360.

**Definitions** Let $ P = \{A, B, C\} \subset \mathbb{R}^2 $ be a set of three distinct points forming the vertices of an isosceles triangle. **Constraints** 1. The triangle is isosceles: exactly two sides have equal length. 2. The apex (vertex opposite the base) is the point where the two equal sides meet. 3. The line of symmetry passes through the apex and the midpoint of the base. 4. The direction vector $ \vec{v} $ is defined as the vector from the midpoint of the base to the apex. 5. The angle $ \theta $ is measured counterclockwise from the positive x-axis $ (1,0) $ to $ \vec{v} $, normalized to $ [0^\circ, 360^\circ) $. **Objective** Compute: $$ \theta = \operatorname{atan2}(v_y, v_x) \cdot \frac{180}{\pi} \mod 360 $$ where $ \vec{v} = \text{apex} - \text{midpoint of base} $, and the apex is identified as the vertex equidistant to the other two.

API Response (JSON)

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      "statement_type": "Markdown",
      "content": "Given the three points that represent the corners of an isosceles triangle, determine the angle that the triangle is pointing. The angle can be calculated based on the vector created along the line of...",
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