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 C_{1}and C_{2}meet at the points A and B. The tangent to C_{1}at A meets C_{2 }at P. A point Q inside C_{1}lies on the circumference of C_{2}. When produced, BQ meets C_{1}at S and PA produced at T. Prove that AS is parallel to PQ.

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