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
In the diagram the length $SP$, $SQ$ and $SR$ are equal and the angle $SRQ$ is $x^\circ$. What is the size (in degrees) of the angle $PQR$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.