Question

Срочно 5. В угол вписана окружность. Точки касания делят ее на две части, которые относятся как 7:11. Найдите данный угол. а) 40. б) 70. в) 110. г) 140. 6. В четырехугольник ABCD вписана окружность, AB=11 см, CD=17 см. Найдите периметр четырехугольника. а) 14 см. б) 28 см. в) 40 см. г) 56 см. 7. Какой наибольший центральный угол может быть у правильного многоугольника, вписанного в окружность? а) 60 . б) 90 . в) 120 . г) Нельзя определить. 8. Периметр правильного шестиугольника, вписанного в окружность, равен 36 см. Найдите диаметр окружности. а) 6 см. б) 9 см. в) 12 см. г) 18 см.

Answer 1

Ответ:

5. Б

6. А

7. Г

8. А

Объяснение:

Answer 2

Question 5: Given that a circle is inscribed in a corner and the points of contact divide it into two parts that are in a ratio of 7:11, we need to find the angle of the corner.

To solve this problem, we can use the property that the angle at the center of a circle is twice the angle at the circumference that is subtended by the same arc.

Let's denote the smaller part of the circle as "7x" and the larger part as "11x." The sum of these two parts is equal to the angle at the center of the circle.

According to the property mentioned above, we can write the equation:

7x + 11x = 360°

Simplifying the equation:

18x = 360°

Dividing both sides by 18:

x = 20°

Now we can find the angle of the corner by multiplying x by 7:

Angle of the corner = 7x = 7 * 20° = 140°

Therefore, the answer is (г) 140°.

Question 6: In the quadrilateral ABCD, a circle is inscribed, and the lengths of AB and CD are given as 11 cm and 17 cm, respectively. We need to find the perimeter of the quadrilateral.

To find the perimeter, we need to know the lengths of the other two sides of the quadrilateral. Unfortunately, the given information does not provide enough information to determine the lengths of the other two sides.

Therefore, it is not possible to determine the perimeter of the quadrilateral based on the given information. The answer is (г) Нельзя определить.

Question 7: We are asked to find the largest central angle that a regular polygon inscribed in a circle can have.

In a regular polygon, all the central angles are equal. The sum of all the central angles in a polygon is equal to 360°.

Let's suppose the number of sides of the polygon is "n." Each central angle would be 360°/n.

To find the largest central angle, we need to find the smallest possible value of "n" for which 360°/n is an integer.

The smallest possible value of "n" for which 360°/n is an integer is when n = 3, which gives us a regular triangle.

Therefore, the largest central angle that a regular polygon inscribed in a circle can have is (а) 60°.

Question 8: Given that the perimeter of a regular hexagon inscribed in a circle is 36 cm, we need to find the diameter of the circle.

A regular hexagon has six equal sides. Let's denote the length of each side as "s."

The perimeter of the hexagon is given as 36 cm, which means:

6s = 36

Dividing both sides by 6:

s = 6 cm

The diameter of the circle is equal to twice the radius of the circle, which is also equal to the length of each side of the hexagon.

Therefore, the diameter of the circle is 2 * 6 cm = (а) 12 cm.