Question

Самостоятельная работа «Вписанный и описанный четырехугольник» Вариант 1 1. Четырехугольник ABCD вписан в окружность. Угол А = 63°. Найдите величину угла С. 2. Четырехугольник ABCD вписан в окружность. Угол А в 2 раза больше угла С. Найдите эти углы. 3. Четырехугольник ABCD описан вокруг окружности. BC = 12, AD = 16. Найдите периметр ABCD. 4. Равнобедренная трапеция ABCD (BC и AD — основания) описана вокруг окружности, радиус которой равен 2. Найдите периметр, площадь и среднюю линию трапеции, если боковая сторона равна 18. -​

Answer 1

Ответ:

98°

Объяснение:∠ABD = ∠ACD = 63° (т.к. эти углы опираются на одну и ту же дугу AD)

Рассмотрим Δ ACD:

∠ACD = 63°,

∠CAD = 35° (по условию) , тогда:

∠ADC = 180° - 63° - 35° = 82° (т.к. сумма углов треугольника равна 180°)Если четырёхугольник вписан в окружность, то суммы величин его противоположных углов равны 180° (теорема).

Значит: ∠ADC + ∠ABC = 180°, откуда:

∠ABC = 180° - ∠ADC

∠ABC = 180° - 82°

∠ABC = 98°

правильно?

Answer 2

Finding the Angle C in a Quadrilateral Inscribed in a Circle

1. The angle A in the quadrilateral ABCD inscribed in a circle is 63°. We need to find the angle C.

The sum of opposite angles in an inscribed quadrilateral is 180°. Therefore, angle C can be found using the formula: C = 180° - A.

Substituting the given value, we get: C = 180° - 63° = 117° [[8 #]].

2. The angle A in the quadrilateral ABCD inscribed in a circle is twice the angle C. We need to find both angles.

Let's denote the angle C as x. Then, according to the given condition, the angle A is 2x.

We can set up the equation: A = 2C.

Substituting the value of A from the previous question, we get: 2x = 63°. Solving for x, we find: x = 31.5°. Therefore, A = 63° and C = 31.5°.

3. The quadrilateral ABCD is circumscribed around a circle, and BC = 12, AD = 16. We need to find the perimeter of ABCD.

The perimeter of a circumscribed quadrilateral can be found using the formula: Perimeter = AB + BC + CD + DA.

Given that BC = 12 and AD = 16, we need to find the lengths of AB and CD. Unfortunately, the provided sources do not contain relevant information to calculate the lengths of AB and CD.

4. The isosceles trapezoid ABCD (BC and AD are the bases) is circumscribed around a circle with a radius of 2. The lateral side is 18. We need to find the perimeter, area, and median of the trapezoid.

To find the perimeter, area, and median of the trapezoid, we need the lengths of the bases and the height. Unfortunately, the provided sources do not contain relevant information to calculate these values.

Unfortunately, the provided sources do not contain the specific geometric properties required to solve questions 3 and 4. If you have access to the full problem statement or additional information, please provide it, and I can assist further.