Círcunferencia inscrita en triángulo rectángulo | Área de la esquina sombreada🧐

The video is a well-structured tutorial that effectively demonstrates a step-by-step approach to solving a classic geometry problem. The instructor’s method is clear and logical, breaking down the problem into manageable parts. He correctly identifies that the shaded area can be found by subtracting a quarter circle from a square, and he uses the Pythagorean theorem to relate the unknown radius to the given side lengths. The algebraic manipulation is thorough, and he explains each step, including the expansion of binomials and factoring, which is helpful for learners. The final answer is correct, and the instructor provides a numerical approximation. The video’s strength lies in its pedagogical clarity and the emphasis on understanding the underlying concepts rather than just memorizing formulas. However, there are a few minor weaknesses. The instructor occasionally makes off-topic remarks and jokes, which, while adding a lighthearted tone, may distract some viewers. Additionally, the video does not cite any external sources or references, which is typical for a tutorial but limits its value as a research resource. The title accurately reflects the content, and the video fulfills its promise of solving the problem. Overall, the video is a valuable educational resource for students learning geometry, offering a clear and correct solution to a common problem. The presentation is engaging, and the instructor’s enthusiasm is contagious. The video could be improved by providing a more formal derivation or referencing standard geometry theorems, but as a tutorial, it excels in making the material accessible.

The title accurately describes the content: solving for the area of the shaded corner in a right triangle with an inscribed circle.

8/10

The video presents a clear, step-by-step geometric problem-solving approach, correctly applying the Pythagorean theorem and algebraic manipulation. The reasoning is sound and the final answer is correct. The presentation is pedagogical and thorough, though it lacks formal citations or references to external sources.

Markers derived by PSI from the transcript: the creator did not define chapters.

• 00:00Introduction of the problem: right triangle with legs 18 cm and 12 cm, and an inscribed circle; shaded area to be found.
• 01:00Explanation of tangent points and equal tangent lengths, using the analogy of an umbrella and a ball.
• 02:00Setting up the problem: denoting the radius as r, and identifying the shaded area as the area of a square minus a quarter circle.
• 03:00Applying the Pythagorean theorem to the right triangle with sides (12+r), (18+r), and hypotenuse 30.
• 04:00Expanding and simplifying the equation to obtain a quadratic equation in r.
• 05:00Solving the quadratic equation by factoring, obtaining r = 6 cm (discarding negative solution).
• 06:00Calculating the shaded area using the formula: area = r^2 - (πr^2)/4, substituting r = 6, and simplifying to 36 - 9π ≈ 7.74 cm².
• 07:00Proposing a similar exercise: finding the area of a semicircle inscribed in an equilateral triangle with side 100 m.

• Matemáticas con Juan - Official Website — The instructor's official website, where additional resources and exercises may be found.
• Telegram Channel — The instructor's Telegram channel for community interaction and updates.
• Playlist: Cálculo de áreas — A playlist of similar area calculation exercises referenced in the video description.

• Incircle and excircles of a triangle — Provides background on inscribed circles in triangles, supporting the geometric concepts used.
• Pythagorean theorem — The theorem is correctly applied in the video to relate the sides of the triangle.