在△ABC中，BC = 3，AC = 4，∠ACB = 90°，以点B为圆心，BC长为半径画弧，与AB交于点D，再分别以A、D为圆心，大于\frac{1}{2}AD的长为半径画弧，两弧交于点E、F，作直线EF，分别交AC、AB于点P、Q，求PQ的长度。选项：A.\frac{1}{2}；B.\frac{3}{4}；C.\frac{5}{4}；D.\frac{10}{3}---**Chart/Diagram Description:** * **Type:** Geometric Diagram illustrating a construction within a right-angled triangle. * **Main Elements:** * **Triangle ABC:** A triangle with a right angle indicated at vertex C by a square symbol. * **Right Angle Symbol:** Present at vertex C. * **Points:** Labeled points A, B, C, D, P, Q, E, F. * **Line Segments:** AC (highlighted/thicker), BC, AB. Segment AC lies along the horizontal axis. Segment BC is vertical. * **Arcs:** * A dashed arc originating from vertex B, intersecting segment AC at point D. The arc suggests points at a fixed distance from B. * Two intersecting arcs above line AB, centered at points Q and P respectively, meeting at point E. * Two intersecting arcs below line AC, centered at points Q and P respectively, meeting at point F. * **Line EF:** A straight line segment passing through points E and F. This line intersects segment AB at point Q and segment AC at point P. * **Construction:** The arcs centered at Q and P forming points E and F indicate that line EF is the perpendicular bisector of the line segment QP. * **Relative Position and Direction:** * Triangle ABC is oriented with the right angle at C, AC horizontal and BC vertical. * D is a point on AC, between A and C. * Q is a point on AB. * P is a point on AC, between A and C, and located to the right of D. * The line EF passes through Q and P. E is located above AB, and F is located below AC.