 # Concurrence of the Median, a Chord and a Diameter of the Incircle

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In the triangle , let the incircle have center and let its points of tangency to the sides , and be points , and , respectively. Let be the midpoint of . Then the lines , and are concurrent. Drag the locators , and to see that this holds for any triangle.

Contributed by: Sumith Nalabolu and Claire Wang (March 2020)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

The incircle of a triangle is the circle contained in the triangle tangent to each of the three sides. Lines are concurrent if they all pass through a common point.

See  for the formulas AreaOfTriangle, Circumcircle and IntersectionofLines.

See  for the formulas Incircle and TangencyPoint.

This was a project for Advanced Topics in Mathematics II, 2019–2020, Torrey Pines High School, San Diego, CA.

References

 J. Warendorff. "The Second Lemoine Circle" from the Wolfram Demonstrations Project—A Wolfram Web Resource. demonstrations.wolfram.com/TheSecondLemoineCircle.

 J. Warendorff. "Collinearity of a Triangle's Circumcenter, Incenter, and the Contact Triangle's Orthocenter" from the Wolfram Demonstrations Project—A Wolfram Web Resource. demonstrations.wolfram.com/CollinearityOfATrianglesCircumcenterIncenterAndTheContactTri.

## Permanent Citation

Sumith Nalabolu and Claire Wang

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