In the rectangle ABCD, AB = 6 and BC = 8. The diagonals AC and BD intersect at O. Point P lies on the diagonal AC such that AP = 1. A line is drawn from B through P and meets AD at S. Let be R a point on AD such that OR is parallel to BS. a) Find the lengths of AS and RD. Hint: Denote AS = x. Use P S k OR and OR k BS to find AR and RD in terms of x. Then, find the value of x. b) Find the areas of 4AOD and 4COD. c) Find the areas of 4AOS and 4AP S. Hint: Consider that 4AOS and 4AOD have the same altitude. Use 4AP S ∼ 4AOR
let k= area and 4=triangle
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