我是初中生，帮我解答此题---**Title:** 暑假几何挑战 (十四) 250817 (Summer Geometry Challenge (14) 250817)
**Answer Requirements:**
1. Use drawing tools for precise drawing; auxiliary lines should be dashed (the diagrams provided in the original problem may not be accurate).
2. The proof process should be detailed and complete, with a clear structure and neat handwriting.
3. You do not need to print the test paper; you can directly draw and answer on A4 paper (or other paper).
**Problem Stem:**
In right triangle ABC, ∠BAC=90°, AB=AC. Point D is a moving point on side BC. Connect AD. Rotate AD counterclockwise by 90° around point A to obtain AE. Connect CE and DE. Point F is the midpoint of DE. Connect CF.
**Sub-questions:**
(1) As shown in Figure 1, express the quantitative relationship between line segment CF and AD with an equation, and explain the reason.
(2) As shown in Figure 2, during the movement of point D, when BD=2CD, extend CF and BA respectively to intersect at point G. Express the quantitative relationship between line segments AG and BC with an equation, and explain the reason.
(3) During the movement of point D, there exists a point P on line segment AD such that the value of PA+PB+PC is minimized. When the value of PA+PB+PC is minimized, the length of AP is m. Please directly express the length of CE using an expression containing m, draw a diagram, and explain the reason.
**Chart/Diagram Description:**
**Figure 1 (图1):**
* **Type:** Geometric figure.
* **Main Elements:**
* A triangle ABC with vertex A at the top-left, B at the bottom-left, and C at the bottom-right.
* Point D is on the line segment BC, between B and C.
* Line segments AB, AC, BC, AD are drawn.
* Line segment AE is drawn from A, to the right and slightly up from AC.
* Line segments CE and DE are drawn.
* Point F is located on the line segment DE, approximately in the middle.
* Line segment CF is drawn.
* **Labels:** A, B, C, D, E, F.
* **Relative Position:** Points B, D, C are collinear. A is the common vertex for AD and AE. F is on DE.
**Figure 2 (图2):**
* **Type:** Geometric figure.
* **Main Elements:**
* Similar to Figure 1, with a triangle ABC, point D on BC, line segments AD, AE, CE, DE, point F on DE, and line segment CF.
* An additional point G is shown.
* The line segment CF is extended upwards and to the left beyond F, intersecting the extension of line segment BA (which is extended upwards and to the left beyond A) at point G.
* **Labels:** A, B, C, D, E, F, G.
* **Relative Position:** Points B, D, C are collinear. G, A, B are collinear, with A between G and B (meaning BA is extended beyond A). G, F, C are collinear, with F between G and C.