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已知正方形ABCDABCD的边长为22，点QQ为边BCBC的中点，点PP在正方形边ADAD外部，且满足∠APD=135∘\angle APD=135^\circ，则PQPQ的最大值

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Solve for a variable using properties of multiplicationright chevron icon

Full solution

Q. 已知正方形ABCDABCD的边长为22，点QQ为边BCBC的中点，点PP在正方形边ADAD外部，且满足∠APD=135∘\angle APD=135^\circ，则PQPQ的最大值
  1. Identify Coordinates: Identify the coordinates of points AA, BB, CC, DD, and QQ.A(0,0)A(0,0), B(2,0)B(2,0), C(2,2)C(2,2), D(0,2)D(0,2); QQ is the midpoint of BB00, so BB11.
  2. Analyze Angle: Analyze the angle ∠APD=135∘\angle APD = 135^\circ. This angle suggests that triangle APDAPD is not a right triangle, and PP must be positioned such that it forms a 135∘135^\circ angle with points AA and DD.
  3. Determine Location for P: Determine the possible location for P. Since ∠APD=135∘\angle APD = 135^\circ, P must lie on the circle with diameter AD that extends beyond point D. The circle's equation based on diameter AD is (x−1)2+(y−1)2=2(x-1)^2 + (y-1)^2 = 2.

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