Problem 17

(i) Given a circle, with points B,C,D,E which lie on its circumference and chords DE and BC intersecting within the circle at F, create a relation, with proof, between the lengths BF, FC, EF and FD.
The diagram can be found below.

(ii) Now given the same circle, but point F now lies outside of the circle (diagram shown below), create a similar relation between DE, BC and CE, with proof.
The diagram can be found below.