Question

У трикутнику АВС основа висоти АК лежить на продовженні сторони ВС. АК =2 ,АС =6. Радіус кола описанного навколо трикутника АВС дорівнює 4,5. Знайдіть довжину відрізка АВ.​

Answer 1

Объяснение:

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Answer 2

Task: Find the length of segment AB in triangle ABC.

To find the length of segment AB in triangle ABC, we can use the given information about the triangle and apply some geometric principles.

Given information: - The base of triangle ABC is BC. - The height of triangle ABC, AK, lies on the extension of side BC. - AK = 2 - AC = 6 - The radius of the circumcircle of triangle ABC is 4.5.

To find the length of segment AB, we can use the fact that the circumradius of a triangle is related to its side lengths. In particular, for a triangle with sides a, b, and c, and circumradius R, the following relationship holds:

a * b * c = 4 * R * (area of the triangle)

Let's apply this relationship to triangle ABC.

The area of triangle ABC can be calculated using the formula:

Area = (1/2) * base * height

In this case, the base is BC and the height is AK. Substituting the given values, we have:

Area = (1/2) * BC * AK

Now, we can substitute the values of BC and AK:

Area = (1/2) * AC * AK

Area = (1/2) * 6 * 2

Area = 6

Now, let's apply the relationship between the side lengths and the circumradius:

AB * BC * AC = 4 * R * Area

Substituting the given values:

AB * 6 * 6 = 4 * 4.5 * 6

AB * 36 = 27

AB = 27 / 36

AB = 3/4

Therefore, the length of segment AB in triangle ABC is 3/4.

Note: The search results provided by You.com did not provide any relevant information for this specific problem. The solution was derived using geometric principles and calculations.