Henry Ernest Dudeney/Modern Puzzles/164 - Those Russian Cyclists Again

Modern Puzzles by Henry Ernest Dudeney: $164$

Those Russian Cyclists Again

Here is another little experience of the two Russian Army motor-cyclists from the last puzzle.

In the section from a map given in the diagram we are shown three long straight roads, forming a right-angled triangle.

The General asked the two men how far it was from $A$ to $B$.

Pyotr replied that all he knew was that riding round the triangle, from $A$ to $B$,

from there to $C$ and home to $A$, his odometer showed exactly $60$ miles,

while Sergei could only say that he happened to know that $C$ was exactly $12$ miles from the road $A$ to $B$ --

that is, to the point $D$, as shown by the dotted line.

Whereupon the General made a very simple calculation in his head and declared that the distance from $A$ to $B$ must be ...

Can the reader discover so easily how far it was?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Unicursal and Route Problems: $164$. -- Those Russian Cyclists Again
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $282$. Those Russian Cyclists Again