解答这个题目---**Extracted Content:** **Question Number:** 2 **Question Stem:** 设MN是圆O外一直线, 过O作OA⊥MN于A, 自A引圆的两条直线, 交圆于B、C与D、E, 直线EB与CD分别交MN于P、Q. 求证: AP=AQ. (初二) **Chart/Diagram Description:** * **Type:** Geometric figure. * **Main Elements:** * **Circle:** A circle with center O is shown. * **Line:** A horizontal line labeled MN passes below the circle. * **Point:** Point A is on the line MN. * **Line Segment:** OA is a vertical line segment connecting the center O to point A on line MN. This segment is labeled as perpendicular (implied by OA⊥MN). * **Points on Circle:** Points B, C, D, E, and G are on the circle. * **Lines from A:** Two lines originate from A and intersect the circle. * One line passes through A, intersects the circle at B and C. Points B and C are on the same side of the line OA. * The other line passes through A, intersects the circle at D and E. Points D and E are on the opposite side of the line OA from B and C. Point D is closer to A than E. * **Lines EB and CD:** Line segment EB connects points E and B. Line segment CD connects points C and D. * **Intersection Points on MN:** Line EB intersects the line MN at point P. Line CD intersects the line MN at point Q. Points P, A, and Q are on the line MN, with P to the left of A and Q to the right of A. * **Point G:** Point G is on the circle vertically above O and on the same side of OA as B and C. A line segment OG is shown (it's a radius). A vertical diameter through O is implied by the position of G. * **Labels:** Points O, A, B, C, D, E, G, M, N, P, Q are labeled. The line MN is labeled. The condition OA⊥MN is stated in the text and depicted by the vertical line OA and horizontal line MN intersecting at A. **Other Relevant Text:** (初二) - This indicates the problem is typically encountered in the second year of junior high school.