i) ABCD is a rhombus. A tangent to the inscribed circle meets AB,DA,BC,CD at M,N,P,Q respectively. Find a relationship between BM and DN.
ii) ABCD is a rhombus and P a point inside. The circles through P with centers A,B,C,D meet the four sides AB,BC,CD,DA in eight points. Find a property of the resulting octagon. Use it to construct a regular octagon.
iii) Rotate the figure about the line AC to form a solid. State a similar result. geometryrhombusoctagonincircleconstruction