You may also like

Set Square

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

Biggest Bendy

Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?

Strange Rectangle 2

Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.

Strange Rectangle

Age 16 to 18
Challenge Level

Rectangle with quadrilateral drawn betweens points on each side.

Show that, for any values of $x$ and $y$ where $x> y$,

  1. the angle $SPQ$ is always the same and find this angle
  2. the angle $SRQ$ is always the same and find this angle
  3. the quadrilateral $SPQR$ is cyclic
  4. the angle $PQR$ is always the same and find this angle
  5. the angle $PSR$ is always the same and find this angle.