Question

Даны две параллельные плоскости и не лежащие между нами точкой Р.Две прямые проходяшые через точку Р плоскость в точке А1А2 а дальнюю в точке В1В2соответственно . Найдите В1В2если АА2=6:РА1:А1В1=3:2

Answer 1

построй рисунок, и посмотри как решать и что дано. увидишь 2 подобных треугольника

Answer 2

I have searched the web for your question and found some relevant results. Here is a detailed answer based on the information from the first result:

The problem is to find the length of the segment B1B2, given two parallel planes and a point P that does not lie between them. Two lines passing through the point P intersect the plane closer to the point P at the points A1 and A2, and the farther plane at the points B1 and B2 respectively. The length of the segment A1A2 is 6 cm and the ratio of PA1 to A1B1 is 3:2.

To solve this problem, we can use the property of similar triangles. The plane of the triangle PB1B2 intersects the given planes. If two parallel planes are intersected by a third plane, then the lines of their intersection are parallel (property). In the triangle PB1B2, the segment A1A2 is parallel to B1B2. Corresponding angles at the parallel A1A2 and B1B2 and the secants PB1 and PB2 are equal, therefore, the triangles PB1B2 and PA1A2 are similar. By the condition, PA1:A1B1=3:2, therefore, PB1=PA1+A1B1=5 parts. B1B2:A1A2=PB1:PA1 B1B2:6=5:3 B1B2=30/3 B1B2=10 cm

Therefore, the length of the segment B1B2 is 10 cm. I hope this helps you understand the solution.