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Suppose a friend asks you: What is the Pythagorean theorem? Write a clear and easy to understand answer to the question. Your grade will depend on the quality of the exposition as well as on mathematical correctness. 1. Show that the three triangles in the figure are similar, and hence prove the Pythagorean theorem by equating ratios of corresponding sides. C1 Prove that in a triangle with side lengths 3, 4, and 5 the radius of the inscribed circle is 1. 2. 3 3. Find the area of the octagon that is inscribed in a circle as shown in the figure. Write your answer in the form r +svt, where r,s,and t are positive integers.

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