Question

Дана окружность с центром О и радиусом 5 см. Проведена хорда АВ равная 6 см. Найдите периметр треугольника АОВ. Пожалуйста, буду очень счастлив​

Answer 1

Ответ:

Треугольник АОВ равнобедренный,т к АО=ОВ,как

радиусы

АО=ОВ=5 см

Р треугольника=5•2+6=16 см

Объяснение:

Answer 2

Perimeter of Triangle AOV

To find the perimeter of triangle AOV, we need to determine the lengths of the sides AO and OV.

Given: - The circle has a center O and a radius of 5 cm. - The chord AB is equal to 6 cm.

To find the length of AO, we can use the Pythagorean theorem. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is AO, and the other two sides are the radius of the circle (5 cm) and half of the chord AB (6 cm/2 = 3 cm).

Using the Pythagorean theorem, we can calculate the length of AO as follows:

AO^2 = (radius)^2 + (half of AB)^2 AO^2 = 5^2 + 3^2 AO^2 = 25 + 9 AO^2 = 34

Taking the square root of both sides, we find:

AO = √34 cm

Now, to find the length of OV, we can subtract the length of AO from the radius of the circle:

OV = radius - AO OV = 5 cm - √34 cm

To calculate the perimeter of triangle AOV, we add the lengths of the three sides: AO, OV, and VA.

Perimeter = AO + OV + VA

Since VA is equal to AB (6 cm), the perimeter can be expressed as:

Perimeter = AO + OV + AB

Let's calculate the values:

AO = √34 cm OV = 5 cm - √34 cm AB = 6 cm

Substituting these values into the perimeter formula, we get:

Perimeter = √34 cm + (5 cm - √34 cm) + 6 cm

Simplifying the expression, we have:

Perimeter = 5 cm + 6 cm Perimeter = 11 cm

Therefore, the perimeter of triangle AOV is 11 cm.

Please let me know if there's anything else I can help you with!