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Construct a Segment with a Given Midpoint and Endpoints on Two Given Lines
Given two lines
and
and a point
, construct a segment
such that
,
and
is its midpoint.
Construction
Choose any point
on
such that
is not perpendicular to
.
Draw a circle
with the center
and the radius
. Let a point
be the second intersection of
and
.
Let
and
be symmetric to
and
with respect to
. Then the quadrilateral
is a rectangle.
Let
be the intersection of
and the line
. Then the point
symmetric to
with respect to
is on
and
is the midpoint of
.
Contributed by:
Marko Razpet
and
Izidor Hafner
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RELATED LINKS
Line Segment
(
Wolfram
MathWorld
)
Midpoint
(
Wolfram
MathWorld
)
Symmetric Points
(
Wolfram
MathWorld
)
PERMANENT CITATION
Marko Razpet
and
Izidor Hafner
"
Construct a Segment with a Given Midpoint and Endpoints on Two Given Lines
"
http://demonstrations.wolfram.com/ConstructASegmentWithAGivenMidpointAndEndpointsOnTwoGivenLin/
Wolfram Demonstrations Project
Published: August 20, 2018
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