请解此题，并制作成辅导视频---**Question 24** (Total points for this question: 12 points) **Problem Description:** As shown in the figure, in Right-angled triangle Rt△ABC, ∠ACB = 90°. D is the midpoint of AB. E is a moving point on BC (not coinciding with endpoints B, C). Connect AE and CD, which intersect at point F. A circle passing through points E, F, D intersects BD at point G (not coinciding with B, D). Connect EG. **(1)** If CE = CF and ∠B = 50°, find the measure of ∠EGD. **(2)** If CE/BE = 1/2, find the value of EF/AF. **(3)** Prove: EG + EF = AF. **Diagram Description:** Type: Geometric figure. Main Elements: * A right-angled triangle ABC with the right angle at vertex C. * Point D is the midpoint of the hypotenuse AB. * A line segment CD connects C to D. * Point E is located on the side BC (between B and C). * A line segment AE connects A to E. * Point F is the intersection of line segments AE and CD. * A circle is drawn passing through points E, F, and D. * This circle intersects the line segment BD at point G. * A line segment EG connects E and G. * Points A, B, C, D, E, F, G are labeled. * The relative positions show A, D, B are collinear, C is above AB, E is on BC, F is inside triangle ABC, and G is on BD. **(End of Question 24)**