Stage 18 · Circles

18.5.5 Incenter Versus Circumcenter, Side by Side

18.5 Tangent Lines — The Line That Only Kisses Once

Point 5 of 5

18.5.5 Incenter Versus Circumcenter, Side by Side

Core idea

The incenter is equidistant from the three sides and always sits inside the triangle, while the circumcenter is equidistant from the three corners and can wander outside it.

Module goal. Dig deep into the borderline case of tangency, mastering a tangent's properties, its test, and the tangent-length theorem, then apply them to a triangle's inscribed circle.
eastmath.com · 18.5 Tangent Lines — The Line That Only Kisses Once · 18.5.5 Incenter Versus Circumcenter, Side by Side