11453
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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
THINGS TO TRY
Slider Zoom
Gamepad Controls
Automatic Animation
SNAPSHOTS
DETAILS
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
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
16. Construct a Triangle Given Its Circumradius, Inradius and the Difference of Its Base Angles
Izidor Hafner
4. Construct a Triangle Given Its Circumradius, Inradius and a Vertex Angle
Izidor Hafner
20. Construct a Triangle Given the Length of Its Base, the Difference of Its Base Angles and a Line Containing the Third Vertex
Izidor Hafner
19. Construct a Triangle Given the Length of Its Base, the Difference of Its Base Angles and a Special Point of Intersection
Izidor Hafner
18. Construct a Triangle Given the Length of Its Base, the Difference of Angles at Its Base and the Point of Intersection of an Angle Bisector with Its Base
Izidor Hafner
26c. Construct a Triangle Given the Length of Its Base, the Angle Opposite the Base and the Length of That Angle's Bisector
Izidor Hafner
5. Construct a Triangle Given Its Circumradius, the Difference of Base Angles and the Sum of the Other Two Sides
Izidor Hafner
26b. Construct a Triangle Given the Length of Its Base, the Angle Opposite the Base and the Length of That Angle's Bisector
Izidor Hafner
25. Construct a Triangle Given Its Base, the Difference of the Base Angles and the Length of One of Three Line Segments
Izidor Hafner
12. Construct a Triangle Given the Length of Its Base, the Perimeter and the Difference of the Base Angles
Izidor Hafner
Related Topics
Plane Geometry
Triangles
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+