The Ratio of a Side of a Triangle to the Corresponding Side of the Orthic Triangle

show R

AC

×

OB''

≈

0.37

AB

×

OC''

≈

0.84

BC

×

OA''

≈

0.97

R

×

A'C'

≈

0.37

R

×

A'B'

≈

0.84

R

×

B'C'

≈

0.97

The ratio of a side of a triangle to the corresponding side of the orthic triangle is equal to the ratio of the circumradius to the distance from the side to the circumcenter. For example,

AB/A'B'=R/OC''

.

Details

See theorem 197 in N. Altshiller-Court, College Geometry, Mineola, NY: Dover, 2007 p. 100.

External Links

Circumcircle (Wolfram MathWorld)

Orthic Triangle (Wolfram MathWorld)

Permanent Citation

Jay Warendorff

"The Ratio of a Side of a Triangle to the Corresponding Side of the Orthic Triangle"
http://demonstrations.wolfram.com/TheRatioOfASideOfATriangleToTheCorrespondingSideOfTheOrthicT/
Wolfram Demonstrations Project
Published: March 7, 2011