Find the radius of the inscribed circle from three triangle sides. The page traces how the inputs become inradius before rounding.
Sides must form a valid triangle. Near degeneracy drives area and inradius toward zero.
For sides 5,7,9, Heron area is about 17.412 and s=10.5, so r≈1.658. This Triangle Inradius example can be compared with circumradius.
The inradius must be positive and smaller than every triangle altitude. Multiplying it by semiperimeter should reconstruct Heron area.
Sketch Side a before running Triangle Inradius. Place Side b on the Triangle Inradius sketch and confirm its unit.
Test a symmetric Triangle Inradius case. In that Triangle Inradius case, compare Side b with the expected Triangle Inradius scale.
Check Triangle Inradius from Side a, then verify Side b. Estimate the Triangle Inradius Inradius before computing it again. If Side c changes during Triangle Inradius, keep Side b fixed. That Triangle Inradius comparison shows whether Inradius moves as expected.
Before using Inradius downstream, substitute a simple Side a into the same Triangle Inradius relation. Preserve Side b so the comparison remains fair. The resulting Inradius provides a benchmark for detecting a misplaced sign, decimal, or input order.
A one-input trial is useful when Triangle Inradius behaves unexpectedly. Change Side c alone, retain Side a and Side b, and observe Inradius. Multiple simultaneous edits would make the cause of the changed Inradius ambiguous within the Triangle Inradius setup.
Preserve the first Triangle Inradius case before testing another value of Side a. Leave Side b unchanged so a shift in Inradius has one cause. Recording both values of Inradius also prevents the revised Triangle Inradius data from replacing the original silently.
Test Triangle Inradius with a round value for Side a. Keep Side b fixed and estimate Inradius before recalculating. The estimated Inradius gives the original Triangle Inradius answer a scale check, while the unchanged Side b makes the comparison meaningful.
Use a familiar benchmark for Side a to challenge the Triangle Inradius output. Apply the same Side b and anticipate Inradius before calculating. This benchmark need not duplicate the problem; it only needs to reveal an implausible Inradius or reversed Triangle Inradius direction.
At the intersection of angle bisectors.
Yes.
Area=rs.
No.