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Here are a few more construction problems to try your hand at.
- Given a semicircle centered at a point
with diameter
, find points
and
on
, and points
and
on
the semicircle such that the quadrilateral
is a square.
- Given a quadrant of a circle (two radii that make an
angle of
and the included arc), construct a new circle
that is inscribed in the quadrant (in other words, the new circle
is tangent to both rays and to the quarter arc of the quadrant).
- Given a point
, a line
that does not
pass through
, and a point
on
, construct a circle passing
through
that is tangent to
at the point
.
- Given two points
and
that both lie on the same
side of a line
, find a point
on
such that
and
make the same angle with
.
- Given two points
and
that both lie on the same
side of line
, find a point
on
such that
is
as small as possible. (Hint: This problem is related to the
construction problem 4. Also remember that the
shortest distance between two points is a line.)
- Given two non-parallel lines
and
and a radius
, construct a circle of radius
that is tangent to
both
and
.
Next: About this document ...
Up: construct
Previous: Three Impossible Constructions
Zvezdelina Stankova-Frenkel
2000-11-13