第三问讲解---大题 满分 10分)
问题提出]
1) 如图 1, AC、BC 为 ⊙O 的两条弦, 连接 OA、OB, 若 ∠AOB = 100°, 则 ∠ACB 的度数为
问题探究]
2) 如图 2, 在 △ABC 中, AB = AC, ∠BAC = 80°, 以 AC 为边向上作 △ADC, 以 BC 为边向下作 △BCE, 使得 ∠D = ∠E = 130°, AD // BE, 试判断 △DAC 与 △ECB 是否相似? 并说明理由.
问题解决】
3) 为了全面落实新课标理念, 促进学习方式转变, 某校拟修建一 座项目式学习基地, 如图 3 所示为该基地的平面规划示意图, 在四边形 OABC 中, OC // AB, ∠B = 45°, 以 O 为圆心, OA 为半径的 圆弧分别交 AB、BC 于点 D、E. ∠AOE = 90°, 规划四边形 OADC 区域为项目实施区, △BCD 区域为 评价反馈区, 其他区域为协作交流区, 根据规划要求, BE = 2CE, 请你判断项目实施区 (四边形 OADC) 的面积与协作交流区 (△BCD) 的面积是否相等? 并说明理由.
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**Diagram Description:**
**图1:**
* Type: Geometric figure (Circle).
* Elements:
* Circle with center labeled O.
* Points A, B, C on the circumference of the circle.
* Line segments (radii) OA and OB connecting the center to points A and B.
* Line segments (chords) AC and BC connecting points on the circumference.
* Angle ∠AOB is marked near the center O, with a label "100°".
* Angle ∠ACB is marked at point C.
* Handwritten annotations: Numbers like "100", "73", "32", "50", "100", "32", "32", "50", "50" are present around the diagram.
**图2:**
* Type: Geometric figure (Triangles).
* Elements:
* Triangle ABC. Sides AB and AC appear to be equal. Angle ∠BAC is at vertex A.
* Triangle ADC constructed adjacent to AC. Angle ∠ADC is at vertex D.
* Triangle BCE constructed adjacent to BC. Angle ∠BEC is at vertex E.
* Line segments AD and BE are shown.
* Labels and Annotations: Vertices A, B, C, D, E are labeled. Angles ∠BAC, ∠ADC, ∠BEC are indicated. Handwritten numbers like "50", "50", "80", "50", "130", "130" are present. AB=AC is implied by the text. ∠BAC=80°, ∠ADC=130°, ∠BEC=130°, AD || BE are stated in the text.
**图3 (第20题图):**
* Type: Planar planning diagram (Geometric figure with regions).
* Elements:
* A region defined by points O, A, B, C. This region is referred to as quadrilateral OABC in the text.
* Line segment OC and AB are shown as parallel (OC // AB).
* Angle at B, ∠B, is marked.
* An arc originating from A, centered at O with radius OA, intersects line segment AB at point D and line segment BC at point E. This implies OD = OA and OE = OA as they are points on the arc from O with radius OA.
* Line segments OD and OE are drawn.
* Angle ∠AOE is marked and labeled as 90°.
* Regions are delineated by the lines and arc.
* Regions are conceptually labeled in the text:
* 四边形 OADC (Quadrilateral OADC) as 项目实施区 (Project Implementation Area).
* △BCD (Triangle BCD) as 评价反馈区 (Evaluation and Feedback Area).
* 其他区域 (Other Region) as 协作交流区 (Collaborative Exchange Area). Based on the diagram and text, the "Other Region" is likely the area OAEB minus the area OADE. It is the area enclosed by O, A, E, B.
* Labels and Annotations: Vertices O, A, B, C, D, E are labeled. Angle ∠B is labeled as 45°. Angle ∠AOE is labeled as 90°. Handwritten marks are present. The relationship BE = 2CE is stated in the text. The parallel relationship OC // AB is stated in the text.
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End of Extraction.