Question

У трикутнику зі сторонами 15 м, 15 м і 24 м вписано коло, центр якого з'єднано з вершинами трикутника. знайдіть площі утворених трикутників.

Answer 1

Ответ:

Объяснение:

Фото

Answer 2

Problem Analysis

We are given a triangle with sides measuring 15m, 15m, and 24m. A circle is inscribed within this triangle, and the center of the circle is connected to the vertices of the triangle. We need to find the areas of the triangles formed by these connections.

Solution

To find the areas of the triangles, we can use the formula for the area of a triangle: A = (1/2) * base * height. In this case, the base of each triangle is one of the sides of the original triangle, and the height is the distance from the center of the circle to the side of the triangle.

To find the height of each triangle, we can use the fact that the radius of the inscribed circle is perpendicular to the side of the triangle it touches. Therefore, the height of each triangle is equal to the radius of the inscribed circle.

To find the radius of the inscribed circle, we can use the formula: r = (a + b - c) / 2, where a, b, and c are the lengths of the sides of the triangle. In this case, a = 15m, b = 15m, and c = 24m.

Let's calculate the radius of the inscribed circle and the areas of the triangles.

Calculation

The radius of the inscribed circle can be calculated as follows: r = (a + b - c) / 2 r = (15m + 15m - 24m) / 2 r = 6m

Now, let's calculate the areas of the triangles using the formula A = (1/2) * base * height.

For the first triangle: Base = 15m Height = 6m A1 = (1/2) * 15m * 6m A1 = 45m²

For the second triangle: Base = 15m Height = 6m A2 = (1/2) * 15m * 6m A2 = 45m²

For the third triangle: Base = 24m Height = 6m A3 = (1/2) * 24m * 6m A3 = 72m²

Answer

The areas of the triangles formed by connecting the center of the inscribed circle to the vertices of the triangle are as follows: - The area of the first triangle is 45m². - The area of the second triangle is 45m². - The area of the third triangle is 72m².

Please let me know if you need any further clarification.