请将图片中的数学题做出讲解视频---**Question Number:** 24. **(Total score 12 points)** **Problem Description:** As shown in the figure, in Right Triangle ABC, ∠ACB=90°, D is the midpoint of AB, E is a moving point on BC (not coinciding with endpoints B, C). Connect AE intersecting CD 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, ∠B=50°, find the measure of ∠EGD:** **(2) If $\frac{CE}{BE} = \frac{1}{2}$, find the value of $\frac{EF}{AF}$:** **(3) Prove: EG+EF=AF.** **Diagram Description:** * **Type:** Geometric diagram illustrating a right triangle and a circle. * **Main Elements:** * Triangle ABC, which is a right triangle with the right angle at vertex C. * Point D is on the hypotenuse AB and is labeled as the midpoint. * Point E is on the side BC, between B and C. * Segment CD is drawn from C to D. * Segment AE is drawn from A to E. * Point F is the intersection of segments AE and CD. * A circle passes through points E, F, and D. * This circle intersects the segment BD (part of AB) at point G. * Segment EG is drawn. * Points A, B, C, D, E, F, G are labeled. * **Angles:** ∠ACB is indicated as a right angle. ∠B is shown. * **Annotations:** The diagram is labeled as being for Question 24.