请用视频讲解第12题---**Question 12:** **Question Stem:** 12、 如图, △ABC为等边三角形, D为形外一点, 且∠ADC=60°, AD=2, CD=3, 则BD的长为_____ **Options:** A. 2 B. √5 C. 3 **Diagram Description (第12题图):** * Type: Geometric figure (Triangle and external point). * Main Elements: * Triangle ABC: Appears equilateral. Sides AB, BC, AC are marked with double dashes, indicating equal length. * Point D: Located outside triangle ABC. * Lines: Segments AD, CD, and BD are drawn. * Labels: Points A, B, C, D. Length AD is labeled as 2. Length CD is labeled as 3. Angle ∠ADC is labeled as 60°. Double dashes on AB, BC, AC indicate equal lengths. * Relative Position: Point D is outside triangle ABC. **Question 13:** **Question Stem:** 13、 如图, 在等边△ABC中, 点D、E都在边BC上, ∠DAE=30°, DE=7. 若 BD:EC =3:5, 则 AD的长为_____ **Diagram Description (第13题图):** * Type: Geometric figure (Triangle with points on a side). * Main Elements: * Triangle ABC: Appears equilateral. Sides AB and AC are marked with single dashes, indicating equal length. Angle ∠ABC is labeled as 60°. * Points D and E: Located on side BC. * Lines: Segments AD and AE are drawn. * Labels: Points A, B, C, D, E. Length of segment DE is labeled as 7. Angle ∠DAE is labeled as 30°. Single dashes on AB and AC indicate equal lengths. Angle ∠ABC is labeled as 60°. Handwritten notes on BC likely relate to lengths based on the ratio BD:EC=3:5 (e.g., 3x, 7, 5x). Other handwritten notes (like B', 13x, etc.) are present but appear to be scratch work. * Relative Position: Points B, D, E, C are collinear on the side BC, in that order from left to right. D is between B and E. E is between D and C. **Diagram for Question 11:** **Diagram Description (第11题图):** * Type: Geometric figure (Right triangle with internal points and lines). * Main Elements: * Triangle ABC: Right-angled at C. The angle at C is marked with a right angle symbol. * Points: D is on side BC. E is on side AC. M is on side AB. N is on segment BE. * Lines: Sides BC, AC, AB. Segments CD, DB (forming BC). Segments AE, EC (forming AC). Segments DM, BE, EN. Dashed segments DE, MN. * Labels: Points A, B, C, D, E, M, N. Right angle symbols at C, M (indicating DM ⊥ AB), N (indicating EN ⊥ BE). Single dashes are on segments CD, DM, AE, EC, indicating equal lengths. Numbers near these segments/points suggest lengths: CD=1, DM=1, AE=1, EC=1, BD=2. This implies AC = AE+EC = 1+1=2, and BC = BD+CD = 2+1=3 (assuming D is between B and C, which it appears to be). Other numbers (1 near C, 1 near A, 2 near B) might be other labels or units, but less clear than segment lengths. * Relative Position: D is on BC. E is on AC. M is on AB. N is on BE. DM is perpendicular to AB. EN is perpendicular to BE. * Other text: "第11题图" (Diagram for Question 11). The question text for this diagram is not provided in the image.