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5. Construct a Triangle Given Its Circumradius, the Difference of Base Angles and the Sum of the Other Two Sides
This Demonstration constructs a triangle
given the circumradius
, the difference of angles
at the base
and the sum
of the lengths of the sides
and
.
Construction
Draw a (blue) circle
with center
, radius
and a diameter
. Let
be a point on
such that
.
Step 1: Draw a (red) circle
with diameter
and center
, the midpoint of
. Let
be on
such that
.
Step 2: Let
intersect
at
.
Step 3: Let
be symmetric to
across
.
Step 4: Draw the triangle
.
Verification
Let
and
.
Let
be symmetric to
across
. Let
be the intersection of
and
.
The angle between the angle bisector from
and the altitude from
is
; also,
.
So
is the bisector of the angle at
. Since
,
and
,
, so
.
Contributed by:
Izidor Hafner
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Reference
[1] D. S. Modic,
Triangles, Constructions, Algebraic Solutions
(in Slovenian), Ljubljana: Math Publishers, 2009, pp. 96.
RELATED LINKS
Circumradius
(
Wolfram
MathWorld
)
Construction of an SSA Triangle
(
Wolfram Demonstrations Project
)
The Plemelj Construction of a Triangle: 1
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Izidor Hafner
"
5. Construct a Triangle Given Its Circumradius, the Difference of Base Angles and the Sum of the Other Two Sides
"
http://demonstrations.wolfram.com/5ConstructATriangleGivenItsCircumradiusTheDifferenceOfBaseAn/
Wolfram Demonstrations Project
Published: June 13, 2017
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