The distance between a and B is 25km. C and D are two villages. Da ⊥ AB is in a and CB ⊥ AB is in B. Da = 15km and CB = 10km are known. The distance between two villages can be calculated Note C and D are not on the same side, they are on both sides of the railway. The distance of CD is actually the total length of the hypotenuse of two small right triangles.

The distance between a and B is 25km. C and D are two villages. Da ⊥ AB is in a and CB ⊥ AB is in B. Da = 15km and CB = 10km are known. The distance between two villages can be calculated Note C and D are not on the same side, they are on both sides of the railway. The distance of CD is actually the total length of the hypotenuse of two small right triangles.

The parallel line of DC crossing point a intersects the extension line BC and E
CE = ad = 15, then be = BC + CE = 10 + 15 = 25
AB = 25, be = 25 in Abe
According to Pythagorean theorem, AE = 25 √ 2
CD=AE=25√ 2

As shown in the figure, on the straight railway, the distance between a and B is 25km, C and D are two villages, Da = 10km, CB = 15km, Da ⊥ AB is in a, CB ⊥ AB is in B. now we need to build a transfer station E on AB, so that the distance between C and D villages and E station is equal. How far should e be built from a?

Let AE = x, then be = 25-x. according to Pythagorean theorem, de2 = ad2 + AE2 = 102 + x2 in RT △ ade, CE2 = BC2 + be2 = 152 + (25-x) 2 in RT △ BCE. From the meaning of the title, we can see: de = CE, so: 102 + X2 = 152 + (25-x) 2, the solution is: x = 15km. (6 points). Therefore, e should be built 15km away from point a

As shown in the figure, the distance between a and B on the railway is 25km, C and D are two villages, Da ⊥ AB is in a, CB ⊥ AB is in B, known Da = 15km, CB = 10km, now we need to build a local product acquisition station E on the railway AB, so that the distance between C and D villages and E station is equal, then how many kilometers should e station be built from a station?

Let AE = XKM, ∵ C and D villages have the same distance to e station, ∵ de = CE, that is, de2 = CE2. According to Pythagorean theorem, we can get 152 + x2 = 102 + (25-x) 2, x = 10. Therefore, e point should be built 10km away from a station

The distance between a and B on the straight line railway is 40km, and C and D are two villages (DA ⊥ AB, CB ⊥ AB, a and B respectively),
Make the distance from village C and D to coal station m equal

Through the midpoint n of CD, make the vertical line of CD, intersect AB at point m, triangle DMN ≌ triangle CMN