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6. Construct a Triangle Given Its Circumradius, Inradius and the Length of Its Base

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This Demonstration constructs a triangle given the circumradius , inradius and the length of the base .

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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 .

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Contributed by: Izidor Hafner (September 2017)
Open content licensed under CC BY-NC-SA

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Reference

[1] D. S. Modic, Triangles, Constructions, Algebraic Solutions (in Slovenian), Ljubljana: Math Publishers, 2009, p. 82.

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