In fact, we just need to master a few key points of this problem. This topic examines the properties of angular bisector, congruent triangles's judgment and properties, similar triangles's judgment and properties, rectangle's judgment and properties, isosceles triangle's judgment and properties, parallel bisector theorem, Pythagorean theorem and other knowledge, which is very comprehensive. The answer is here/exercise/math /79972 1/? Cz asked for adoption. Honey, don't forget.

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As shown in the figure, in the plane rectangular coordinate system, the straight line L is parallel to the X-axis and intersects with the Y-axis at point A, the point B in the first quadrant is on L, connecting OB, the moving point P satisfies the angle APQ=90 degrees, and PQ intersects with the X-axis at point C. 。

(1) When the moving point P coincides with point B, if the coordinate of point B is (2, 1), find the length of PA.

(2) When the moving point P is on the extension line of line segment OB, if the ordinate of point A is equal to the abscissa of point B, find the value of PA:PC.