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A Sameness Surely

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

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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?

Angle Trisection

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
We haven't received any solutions to this one yet. Here's a copy of one of the diagrams from the Hint, and a suggestion.

You need to show that the angle has been trisected, which would mean angles CBR, RBQ and QBP are equal. Congruent triangles may help you to show this!