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Encircling

An equilateral triangle is sitting on top of a square. What is the radius of the circle that circumscribes this shape?

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Three Balls

A circle has centre O and angle POR = angle QOR. Construct tangents at P and Q meeting at T. Draw a circle with diameter OT. Do P and Q lie inside, or on, or outside this circle?

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Angle Trisection

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

A Sameness Surely

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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


[Geometry problem -- Required Image]