Question

В прямоугольном треугольнике АВС с прямым углом С известны катеты:АС=6,ВС=8.Найдите медиану СК этого треугольника.Решите пожалуйста с подробнымрешением!

Answer 1

Есть свойства: в прямоугольном треугольнике радиус описанной окружности  равен половине гипотенузы, а по другому свойству радиус описан. окружности равен медиане, проведенной к гипотенузе.
Получается гипотенуза АВ по теореме Пифагора 6²+8²=100=10²
АВ=10 см.
R=1/2 АВ=5 см Медиана СК=R=5 см

Answer 2

Finding the Median of Triangle ABC

To find the median CK of the right-angled triangle ABC, we can use the formula for the length of a median in a right-angled triangle. The formula states that the length of a median in a right-angled triangle is equal to half the length of the hypotenuse.

In this case, the hypotenuse of triangle ABC is AC, and the length of AC can be found using the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's calculate the length of the hypotenuse AC first:

Using the given information: - AC is the hypotenuse of triangle ABC. - AC is opposite the right angle at C. - The lengths of the two legs are AC = 6 and BC = 8.

We can apply the Pythagorean theorem to find the length of AC:

AC^2 = AB^2 + BC^2 Substituting the given values: AC^2 = 6^2 + 8^2

Simplifying: AC^2 = 36 + 64 AC^2 = 100

Taking the square root of both sides: AC = 10 Now that we know the length of the hypotenuse AC, we can find the length of the median CK. The median CK is equal to half the length of the hypotenuse AC:

CK = AC / 2 CK = 10 / 2 CK = 5 Therefore, the length of the median CK of triangle ABC is 5.

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