Angles, Polygons and Geometrical Proof Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Angles, Polygons and Geometrical Proof Age 11-14 and Age 14-16.

Printable worksheets containing selections of these problems are available here:

Stage 3 ★ Sheet 1 Solutions
  Sheet 2 Solutions
  Sheet 3 Solutions
  Sheet 4 Solutions
     
Stage 3 ★★ Sheet 1 Solutions
  Sheet 2 Solutions
  Sheet 3 Solutions
     
Stage 4 ★★ Sheet 1 Solutions
  Sheet 2 Solutions
     
Stage 4 ★★★ Sheet 1 Solutions

Circular Inscription

Age 14 to 16 Short
Challenge Level

In the diagram, the radius of the circle is equal to the length AB. Can you find the size of angle ACB?

Two Equilateral Triangles

Age 14 to 16 Short
Challenge Level

Prove that these two lengths are equal.

Griddy Region

Age 14 to 16 Short
Challenge Level

Weekly Problem 34 - 2008
What is the area of the region common to this triangle and square?

Garden Fence

Age 14 to 16 Short
Challenge Level

Weekly Problem 44 - 2009
A garden has the shape of a right-angled triangle. A fence goes from the corner with the right-angle to a point on the opposite side. How long is the fence?

Overlapping Annuli

Age 14 to 16 Short
Challenge Level

Just from the diagram, can you work out the radius of the smaller circles?