10-11.8

Part of 2021 Sharygin Geometry Olympiad

Problems(1)

locus of endpoints of auto able to move on 2 different angles to the right

Source: 2021 Sharygin Geometry Olympiad Finals grades X-XI p8

On the attraction "Merry parking", the auto has only two position* of a steering wheel: "right", and "strongly right". So the auto can move along an arc with radius

r_1

r_2

. The auto started from a point

A

to the Nord, it covered the distance

\ell

and rotated to the angle

a < 2\pi

. Find the locus of its possible endpoints.

geometryLocusarc