1. The vertex E of a square EFGH is inside a square ABCD. The vertices F, G and H are outside the square ABCD. The side EF meets the side CD at X and the side EH meets the side AD at Y. If EX = EY, prove that E lies on BD.
2. Two circles C1 and C2 meet at the points A and B. The tangent to C1 at A meets C2 at P. A point Q inside C1 lies on the circumference of C2. When produced, BQ meets C1 at S and PA produced at T. Prove that AS is parallel to PQ.
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