  For a circle $ C $ contained in the unit disk, the necessary and sufficient
condition for the existence of a triangle inscribed in the unit circle and
circumscribed about $ C $ is known as Chapple's formula. The geometric
properties of Blaschke products of degree 3 given by Daepp et al. (2002) and
Frantz (2004) allow us to extend Chapple's formula to the case of ellipses in
the unit disk. The main aim of this paper is to provide a further extension of
Chapple's formula. Introducing a Blaschke-like map of a domain whose boundary
is a conic, we extend their results to the case where the outer curve is an
ellipse or a parabola. Moreover, we also give some geometrical properties for
the Blaschke-like maps of degree $ d $.
