5. 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.

 

Here is the construction:

 

 

Th

 

 

Proof:

 

Note: DP = DH since triangles BDH and BDP are congruent

Similarly, EQ = EH and RF = FH.

was proved here.

 

Thus,