MathDB

G10

Part of 2021-IMOC

Problems(1)

Show that (IDP) and (IHX) are tangent to each other

Source: IMOC 2021 G10

8/11/2021
Let OO, II be the circumcenter and the incenter of triangle ABCABC, respectively, and let the incircle tangents BCBC at DD. Furthermore, suppose that HH is the orthocenter of triangle BICBIC, NN is the midpoint of the arc BACBAC, and XX is the intersection of OIOI and NHNH. If PP is the reflection of AA with respect to OIOI, show that ⊙(IDP)\odot(IDP) and ⊙(IHX)\odot(IHX) are tangent to each other.
geometrytangent circlesCircumcenterincenter