请解题---**Extraction Content:** **Problem Title:** 例题 10 **Question Stem:** 四边形 ABCD 的两条对角线垂直且相交于点 O, OM、ON 分别与 AB、AD 垂直, 延长 MO、NO, 分别与 CD、BC 交于点 P、Q, 求证: PQ // BD **Requested Proof:** PQ // BD **Diagram Description:** The diagram shows a quadrilateral ABCD. Its diagonals AC and BD intersect at point O, and are perpendicular to each other. There is a point M on AB such that OM is perpendicular to AB. There is a point N on AD such that ON is perpendicular to AD. The line segment MO is extended to intersect the side CD at point P. The line segment NO is extended to intersect the side BC at point Q. Right angle symbols are shown at M (∠OMA or ∠OMB) and N (∠ONA or ∠OND). **Handwritten Calculations/Steps (Partial Solution/Hints):** BQ/QC = S△BOQ / S△AQC DP/PC = S△OPD / S△CPO S△BOQ / S△AQC = (sin∠BOQ * BO * OQ) / (sin∠QOC * OC * OQ) = (sin∠AOD * BO) / (sin∠AOB * OC) S△OPD / S△CPO = (sin∠POD * PO) / (sin∠COP * CO) = (sin∠AOB * DO) / (sin∠AOD * CO)