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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

A classical Greek problem was to find a way to trisect an angle using just a ruler and a pair of compasses. However, this is impossible.

It is possible though, to trisect an angle using a carpenter's square, as demonstrated by the interactivity below.

Can you explain why this works?

Can you extend the idea to trisect an obtuse angle?

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