以上图的题为例，在圆中利用圆的性质和直角三角形，解决线段最值问题的例题。---**Other Relevant Text:** 综合素养提升 **Question Stem:** 11. 如图24-X-9, 以点 G(0,1) 为圆心, 2 为半径的圆与 x 轴交于 A, B 两点, 与 y 轴交于 C, D 两点, E 为 ⊙G 上一动点, CF ⊥ AE 于点 F, 连接 FG, 则弦 AB 的长度为 __________; 点 E 在 ⊙G 上运动的过程中, 线段 FG 的长度的最小值为 __________. **Fill-in-the-blanks (Provided answers in image):** * 弦 AB 的长度为: 2√3 * 线段 FG 的长度的最小值为: √3-1 **Chart/Diagram Description:** * **Type:** Cartesian coordinate system with a circle and various points and line segments. * **Main Elements:** * **Coordinate Axes:** X-axis (horizontal, labeled 'x'), Y-axis (vertical, labeled 'y'). The intersection of the axes is the origin, labeled 'O'. * **Circle:** A circle is drawn. * **Center:** The center of the circle is point G, located on the y-axis at coordinates (0,1). * **Radius:** The radius of the circle is 2. This is implied by the text and indicated by the segment from G to B, which has a length of 2 units (B appears to be at (√3,0) or (2,0) if G was (0,0), but with G(0,1) and radius 2, B is at (x,0) where x^2 + (0-1)^2 = 2^2, so x^2+1=4, x^2=3, x=√3. So B is at (√3,0) and the '2' annotation near B on the x-axis is likely referring to the radius value.) * **Points:** * **G:** Center of the circle, located at (0,1). * **O:** Origin (0,0). * **A, B:** Two points where the circle intersects the x-axis. A is on the negative x-axis, B is on the positive x-axis. * **C, D:** Two points where the circle intersects the y-axis. C is above G, D is below G. * **E:** A point on the circumference of the circle (a "moving point"). * **F:** The foot of the perpendicular from C to the line segment AE. * **Lines/Segments:** * **AB:** A horizontal chord of the circle, lying on the x-axis. * **CD:** A vertical chord of the circle, lying on the y-axis. * **AE:** A chord connecting points A and E. * **CF:** A line segment from C to AE, forming a right angle at F. * **GF:** A line segment connecting the center G to point F. * **GB:** A radius connecting G to B. * **GE:** A radius connecting G to E. * **GC:** A radius connecting G to C. * **Angles:** * ∠CFE is a right angle (indicated by the right-angle symbol at F). * **Labels and Annotations:** * The diagram is titled "图 24-X-9". * The coordinate '1' is marked on the y-axis, corresponding to the y-coordinate of G. * The number '2' is marked near point B on the x-axis, which likely denotes the radius length.