Question

Точка М - середина стороны АВ треугольника АВС и СМ перпендикулярна АВ . Найдите АС если ВС =8см

Answer 1

Ответ:АС=8 см

Пошаговое объяснение:В ΔАВС СМ- медиана и высота по условию ⇒Δ АВС-равнобедренный  по признаку и АС=ВС= 8 см. Ответ: АС=8 см.

Answer 2

Problem Analysis

We are given a triangle ABC, where M is the midpoint of side AB and SM is perpendicular to AB. We need to find the length of AC, given that BC = 8 cm.

Solution

To solve this problem, we can use the concept of similar triangles. Let's consider triangle ABC and triangle SMC.

Since M is the midpoint of AB, we can conclude that AM = MB. Therefore, triangle AMC is an isosceles triangle.

Since SM is perpendicular to AB, we can conclude that angle SMC is a right angle.

Using these two pieces of information, we can conclude that triangle AMC and triangle SMC are similar triangles.

Now, let's use the concept of similar triangles to find the length of AC.

According to the property of similar triangles, the ratio of corresponding sides of two similar triangles is equal.

Therefore, we can write the following proportion:

AC / SM = AM / MC

Since AM = MB and MC = BC - BM, we can substitute these values into the proportion:

AC / SM = AM / (BC - AM)

Substituting the given values, we have:

AC / SM = AM / (8 - AM)

Now, let's solve this proportion to find the value of AC.

Cross-multiplying, we get:

AC * (8 - AM) = SM * AM

Expanding, we have:

8AC - AC * AM = SM * AM

Rearranging the equation, we get:

8AC = AC * AM + SM * AM

Factoring out AM, we have:

8AC = AM * (AC + SM)

Finally, solving for AC, we get:

AC = (AM * (AC + SM)) / 8

Now, let's substitute the given values and solve for AC.

Calculation

Given: BC = 8 cm

We need to find: AC

Let's assume that AM = x cm.

Since M is the midpoint of AB, we have:

AM = MB = x cm

Substituting the given values into the equation, we have:

AC = (x * (AC + SM)) / 8

Now, let's substitute the given value of BC = 8 cm into the equation:

AC = (x * (AC + SM)) / 8

AC = (x * (AC + SM)) / 8

Answer

The length of AC is (x * (AC + SM)) / 8 cm.

Please note that we need the value of SM to calculate the length of AC. The value of SM is not provided in the question.