The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
Prove that the internal angle bisectors of a triangle will never be
perpendicular to each other.
Triangle ABC has a right angle at C. ACRS and CBPQ are squares. ST
and PU are perpendicular to AB produced. Show that ST + PU = AB
This problem is taken from the UKMT Mathematical Challenges.