MathDB

i) Show that a regular hexagon, six squares, and six equilateral triangles can be assembled without overlapping to form a regular dodecagon. ii) Let

P_1 , P_2 ,\ldots, P_{12}

be the vertices of a regular dodecagon. Prove that the three diagonals

P_{1}P_{9}, P_{2}P_{11}

and

P_{4}P_{12}

intersect.

A1