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6. Construct a Triangle Given Its Circumradius, Inradius and the Length of Its Base
This Demonstration constructs a triangle
given the circumradius
, inradius
and the length of the base
.
Construction
Draw a circle
of radius
and a chord
of length
.
Step 1: Let
be the midpoint of
and let the right bisector of
meet
at the point
.
Step 2: Draw a second circle
with center
through
and
. Draw a (green) line
perpendicular to
at
so that
. Clearly
is parallel to
.
Step 3: Let
be one of the points of intersection of
and
. The point
is the intersection of
and the ray
.
Verification
Let
,
and
.
Since arc
equals arc
,
bisects
and
. Also
. The triangle
is isosceles, so
. Then
. So
is the incenter of
with distance
from
.
Contributed by:
Izidor Hafner
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Reference
[1] D. S. Modic,
Triangles, Constructions, Algebraic Solutions
(in Slovenian), Ljubljana: Math Publishers, 2009, p. 82.
RELATED LINKS
Inradius
(
Wolfram
MathWorld
)
Circumradius
(
Wolfram
MathWorld
)
The Plemelj Construction of a Triangle 1
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Izidor Hafner
"
6. Construct a Triangle Given Its Circumradius, Inradius and the Length of Its Base
"
http://demonstrations.wolfram.com/6ConstructATriangleGivenItsCircumradiusInradiusAndTheLengthO/
Wolfram Demonstrations Project
Published: September 8, 2017
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