Question

2. В окружности проведена Хорда ВА,стягивающая дугу в 126° , и диаметр ВС. Найдите угол АВС. ( объясните,пожалуйста,как чертёж нарисовать.) 3) Хорда АВ делит окружность на две дуги,меньшая из которых равна 110°.На большей дуге взята точка С так,что дуга АС:дугу СВ = 13:12. Найдите угол САВ. ( объясните,пожалуйста,как чертёж нарисовать.)

Answer 1

1) Хорда BA делит окружность на две дуги,одна из которых равна 126,диаметр AB делит окружность на две дуги,одна из которых равна 180,а другая x,наглядно видно,что получается три дуги - одна в 126 градусов,другая - в 180,третья - в x.Сумма дуг окружностей равна 360 градусам,т.е 360-180-126=x=54,дуга AC равна 54,а вписанный угол ABC равен,как известно,половине дуги,на которую он опирается,т.е угол ABC=27. 2) Хорда AB делит окружность на две дуги,одна равна 110,а другая - 250,вот эта большая дуга,равная 250,делится точкой C на две дуги - 12x и 13x (всегда можно записать пропорциональность в таком виде,например, в отношении 1/2 - это x и 2x) , т.е 25x=250,x=10,вписанный угол CAB опирается на "дугу 13x",т.е на дугу,равную 130 градусам,т.е он равен 65 градусам.

Answer 2

Task 2: Finding Angle AVS in a Circle with Chord VA and Diameter VC

To find the angle AVS, we need to consider the relationship between the chord VA and the diameter VC.

Let's start by drawing a circle with the chord VA and the diameter VC. To do this, follow these steps:

1. Draw a circle with a center point O. 2. Draw a diameter VC passing through the center O. 3. Draw a chord VA that stings the arc with a measure of 126°.

Now, to find the angle AVS, we need to find the measure of the arc VS. Since the chord VA stings the arc with a measure of 126°, the arc VS will have a measure of 360° - 126° = 234°.

Next, we can find the angle AVS by considering that the angle formed by an arc at the center of a circle is twice the angle formed by the same arc at any point on the circumference. Therefore, the angle AVS will be half the measure of the arc VS.

So, the angle AVS = 234° / 2 = 117°.

Task 3: Finding Angle SAV in a Circle with Chord AB and Point C on the Larger Arc

To find the angle SAV, we need to consider the relationship between the chord AB and the point C on the larger arc.

Let's start by drawing a circle with the chord AB and the point C on the larger arc. To do this, follow these steps:

1. Draw a circle with a center point O. 2. Draw a chord AB. 3. Place the point C on the larger arc, such that the ratio of the arc AC to the arc CB is 13:12.

Now, to find the angle SAV, we need to find the measure of the arc SC. Since the ratio of the arc AC to the arc CB is 13:12, we can assign variables to these arcs. Let's say the measure of arc AC is 13x and the measure of arc CB is 12x.

Since the sum of the measures of the arcs AC and CB is equal to the measure of the whole circumference (360°), we can set up the following equation:

13x + 12x = 360°

Simplifying the equation, we get:

25x = 360°

Solving for x, we find:

x = 360° / 25 = 14.4°

Now, we can find the measure of arc SC by subtracting the measures of arcs AC and CB from the whole circumference:

360° - (13x + 12x) = 360° - (13 * 14.4° + 12 * 14.4°) = 360° - (187.2° + 172.8°) = 360° - 360° = 0°

Since the measure of arc SC is 0°, the angle SAV will also be 0°.

Therefore, the angle SAV = 0°.

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