Question

У трикутнику АВС вписане коло із центром і. АВ=6 см, ВС=8 см, АС=10 см Знайти МС, СL, LB, АК, КВ, АМ, МС пожалуста очень срочно!!!! ДАЮ 20 БАЛІВ \ Тема: Коло вписане в трикутник.

Answer 1

Объяснение:

1)AB=6см,BC=8см,AC=10см (за умовою задачі)

CL, LB=1/2×BC. CL=4см, LB=4см.

AK=1/2×AC=5см

Нехай MC-сторона ∆AMC.

MC=одна зі сторін прямокутного трикутника AMC.

MC²=AC²-AM² (за теоремою Піфагора)

AM=1/2×AB=3см

MC²=10²-3²=100-9=91

MC²=91

MC=9,5

Нехай KB- одна зі сторін ∆ABK

KB²=AB²-AK²

KB²=6²-5²=11

KB²=11

KB=3,3см

Відповідь: MC-9,5cm,CL=4cm,LB=4cm,AK=5cm,KB=3,3cm;AM=3cm

Answer 2

Problem Analysis

We are given a triangle ABC with an inscribed circle with center O. The lengths of the sides of the triangle are AB = 6 cm, BC = 8 cm, and AC = 10 cm. We need to find the lengths of various line segments in the triangle.

Solution

To solve this problem, we can use the properties of a triangle with an inscribed circle. Here are the steps to find the lengths of the line segments:

1. Find the radius of the inscribed circle using the formula: radius = (area of the triangle) / (semiperimeter of the triangle). 2. Find the semiperimeter of the triangle using the formula: semiperimeter = (AB + BC + AC) / 2. 3. Find the area of the triangle using Heron's formula: area = sqrt(semiperimeter * (semiperimeter - AB) * (semiperimeter - BC) * (semiperimeter - AC)). 4. Substitute the values of AB, BC, and AC into the formulas to find the radius and area of the inscribed circle. 5. Use the properties of a triangle with an inscribed circle to find the lengths of the line segments.

Let's calculate the values step by step:

1. Find the semiperimeter: - AB = 6 cm - BC = 8 cm - AC = 10 cm - Semiperimeter = (AB + BC + AC) / 2 = (6 + 8 + 10) / 2 = 12 cm

2. Find the area of the triangle: - Semiperimeter = 12 cm - Area = sqrt(semiperimeter * (semiperimeter - AB) * (semiperimeter - BC) * (semiperimeter - AC)) - Area = sqrt(12 * (12 - 6) * (12 - 8) * (12 - 10)) - Area = sqrt(12 * 6 * 4 * 2) - Area = sqrt(576) - Area = 24 cm^2

3. Find the radius of the inscribed circle: - Radius = Area / Semiperimeter = 24 / 12 = 2 cm

Now, let's find the lengths of the line segments:

- MS = SL = LB = Radius = 2 cm (since they are all radii of the inscribed circle). - AK = KV = AM = MC = Radius + Radius = 4 cm (since they are the sum of a radius and a radius). - Note: The lengths of the line segments AK, KV, AM, and MC are equal because they are tangents drawn from the same point to the inscribed circle.

Therefore, the lengths of the line segments are as follows: - MS = SL = LB = 2 cm - AK = KV = AM = MC = 4 cm

I hope this helps! Let me know if you have any further questions.