Assignment 8: Circumcircle and Sums of Ratios of Altitudes

by Shawn Broderick

I have chosen to do Problem 11 of Assignment 8. Here is a refresher of the problem description from the class website:

11. Construct any acute triangle ABC and its circumcircle. Construct the three altitudes AD, BE, and CF. Extend each altitude to its intersection with the circumcircle at corresponding points P, Q, and R.

Find

and prove your result.

Again we have a fun GSP investigation:

assignment8.gsp