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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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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?