Question

Пожалуйста!!!!!!!!! ABCD прямоугольная хоккейная площадка с бортом по периметру. Шайба (точка) находится на стороне АВ на расстоянии 1 от точки А. Требуется ударить по шайбе так, чтобы она ударилась в некоторую точку X на стороне BC. Затем, отскочив, ударилась о борт CD, после чего попала точно в середину стороны AD. Все «отскоки» происходят по принципу «угол падения равен углу отражения», а лёд на площадке идеально гладкий. Найти длину отрезка BX, если известно, что AB = 11, AD = 21. }​

Answer 1

Ответ:

Условие сложное но ответ простой: 10 сантиметров

Answer 2

To find the length of segment BX, we can use the principle of reflection and the fact that the angle of incidence is equal to the angle of reflection. Let's break down the problem step by step.

Given Information:

- AB = 11 - AD = 21

Solution:

1. Let's start by drawing a diagram of the hockey rink with the given points and segments. We have a rectangular hockey rink with sides AB, BC, CD, and AD. The puck starts at point A and needs to hit point X on side BC before bouncing off the board CD and reaching the midpoint of side AD.

2. Since the angle of incidence is equal to the angle of reflection, we can draw a line perpendicular to side BC at point X. Let's call this line MX.

3. Now, let's draw a line perpendicular to side AD at its midpoint. Let's call this line MY.

4. Since the puck hits the midpoint of side AD after bouncing off the board CD, we can draw a line from point X to the midpoint of side AD. Let's call this line XY.

5. We can see that triangle MXY is similar to triangle ABX. This is because angle MXA is equal to angle BXA (both are right angles), and angle MXY is equal to angle BAX (both are alternate angles).

6. Using the property of similar triangles, we can set up the following proportion:

MX / AB = XY / BX

Substituting the given values, we have:

MX / 11 = XY / BX

7. We know that MX is equal to AD (21) and XY is equal to CD (which we need to find). So, we can rewrite the proportion as:

AD / AB = CD / BX

Substituting the given values, we have:

21 / 11 = CD / BX

8. Now, we can solve for BX:

BX = (11 * CD) / 21

To find the value of CD, we need to find the length of segment AD. Using the Pythagorean theorem, we can calculate the length of AD:

AD = sqrt(AB^2 + BD^2)

Substituting the given values, we have:

AD = sqrt(11^2 + 21^2) = sqrt(121 + 441) = sqrt(562) ≈ 23.73

Now, we can substitute the value of AD into the equation for BX:

BX = (11 * CD) / 21

**BX = (11 * CD)