Math Problem Statement

The image contains geometry problems involving triangles, circles, and squares with tasks such as finding distances, calculating radii, and determining areas.

Solution

Let me analyze the uploaded image and extract its mathematical content to assist you with solving the problems. One moment, please.The image contains a set of geometry problems, written in Vietnamese, involving triangles, circles, and tangents. I'll break it down for clarity:


Problem Overview

  1. Geometry Problem 1:

    • A triangle ABC\triangle ABC is given.
    • The radius of the incircle is 2 cm.
    • BC=8cmBC = 8 \, \text{cm}.
    • Find the distance between the incenter II and side BCBC.
  2. Geometry Problem 2:

    • Square Geometry:
      • A square ABCDABCD is drawn.
      • There are additional constructions such as circles and other intersecting geometric shapes within the square.
      • The task involves calculating the areas or distances between points.
  3. Other Details:

    • A problem related to calculating the radius of a circumcircle.
    • Trigonometric calculations appear for specific triangle segments.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Circles
Tangents
Squares

Formulas

Area of triangle = (1/2) × base × height
Pythagoras theorem: a^2 + b^2 = c^2
Distance from a point to a line formula

Theorems

Pythagorean Theorem
Properties of tangents
Incircle and circumcircle properties

Suitable Grade Level

Grades 8-10