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 .

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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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