Sine, cosine, tangent

What is an AC voltage? How much power does an AC power source supply?

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.

What are the shortest distances between the centres of opposite faces of a regular solid dodecahedron on the surface and through the middle of the dodecahedron?

Three squares are drawn on the sides of a triangle ABC. Their areas are respectively 18 000, 20 000 and 26 000 square centimetres. If the outer vertices of the squares are joined, three more triangular areas are enclosed. What is the area of this convex hexagon?

Describe how to construct three circles which have areas in the ratio 1:2:3.

On a nine-point pegboard a band is stretched over 4 pegs in a "figure of 8" arrangement. How many different "figure of 8" arrangements can be made ?

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.