impossipuzzle

[ddon]

"here we are on this straight road between Torsdorf and Elven. Kurt's place is only 21 kilometres from us, but there's no road. We have to go via Elven or Torsdorf. It looks the same distance either way, Linda said. Let's take Elven. Alright, in fact it is exactly the same, John told her. Kurt is just 19 kilometres from there, but 34 from Torsdorf."
How far is Torsdorf from Elven?

[danij]

the answer is 45 km
using complicated maths
apollonius theorem
Draw a triangle
if AC is 34 km dist from torsdorf to kurt
AB is 19 km dist from elven to kurt.
if D is where you are on the side BC.
Let y be the dist drom D to torsdof then BD is y +15
Apollonius theoem then states
y AB^2 +(y+15)AC^2= yBD^2+(y+15)DC^2+(2y+15)AD^2

Solving this equation gives y =15
the dist from torsdorf to elven is y+15 +y =45

[ddon]

WOW! (where did the original 15 come from?)

[danij]

the distances are the same so let the distance from D to
elven be x then the dist from D to kurt is x+19
let the distance from D to torsdorf be y then the distance from D to kurt is y +34
but these distances are the same so
x+19 =y+34
therefore x=y+34-19 i.e. x=y+15

[ddon]

Aaah! Thanks again