What you’ll learn
Construct/understand triangle incircle.
Key idea
Two internal vertex angle bisectors meet at the center of the incircle.
Use distances to side lines, not vertices; in these examples the circumcenter lies on a side and cannot center a positive incircle.
Worked example
Enter the exact value or ordered values in the format requested below.
Right triangle ABC has A=(-3, 2), B=(27, 2), C=(-3, 74), with a right angle at A. Construct its incircle with angle-bisector intersection named I. Enter bisectors=...; center=...; radius=...; tangent=... . Use a perpendicular-to-side radius and all three sides.
- Internal angle bisectors meet at I=(9, 14); its distances to the two leg lines are 12.
- For BC the line-distance numerator equals 12*39, so its distance is also 12; this radius produces all three tangencies.
Answer: bisectors=A,B; center=I; radius=perp(I,AB); tangent=AB,BC,CA
Quick Check
Choose which candidate representation satisfies the requirements of 'Construct/understand triangle incircle' and justify the choice.
Right triangle ABC has A=(0, 0), B=(84, 0), C=(0, 80), with a right angle at A. Candidate 1 uses internal angle bisectors at I=(24, 24) and perpendicular radius to AB. Candidate 2 uses side bisectors at O=(42, 40) with vertex radius OA. Candidate 3 uses midpoint of AB. Select a plan tangent internally to all sides and justify it.