How this calculation works
Find the radius of the circle through the side midpoints and feet of the altitudes.
THE FORMULA
r₉=R/2A worked example
A circumradius of 10 gives nine-point radius 5.
Good to know
Applies to a nondegenerate Euclidean triangle.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Find the radius of the circle through the side midpoints and feet of the altitudes.
The primary result is labeled “Nine-point radius”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Applies to a nondegenerate Euclidean triangle.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
A circumradius of 10 gives nine-point radius 5.
Which rule does this calculator apply?
r₉=R/2