\n ## Geometry Problem: Angle Calculation ### Overview The image presents a geometry problem involving a circle with center O, a diameter AB, a point C on the circle, and a point D. The problem states that angle ∠D = 62° and asks for the measure of angle ∠ACO. The image includes a diagram illustrating the described geometric setup and a step-by-step solution in Chinese. ### Components/Axes The image contains: * A circle with center labeled 'O'. * A diameter AB. * A point C on the circumference of the circle. * A point D on the circumference of the circle. * Angle ∠D labeled as 62°. * Angle ∠ACO, which is the target to be calculated. * Text in Chinese explaining the solution steps. * Multiple choice answers: A. 26°, B. 28°, C. 30°, D. 32° ### Content Details The solution steps, transcribed from the image (Chinese with English translation): 1. **分析与条件:** (Analysis and Conditions) * AB是直径，所以∠ACB = 90° (圆周角定理)。 (AB is a diameter, therefore ∠ACB = 90° (property of inscribed angles)). * ∠D = 62°. 2. **利用圆周角定理:** (Using the Inscribed Angle Theorem) * ∠AOC是圆心角，等于2倍的圆周角∠D。 (∠AOC is a central angle, equal to twice the inscribed angle ∠D). * ∠AOC = 2 × 62° = 124°. 3. **计算∠ACO:** (Calculating ∠ACO) * ∠ACO是三角形AOC的内角。 (∠ACO is an interior angle of triangle AOC). * ∠AOC + ∠CAO + ∠ACO = 180°. * 因为OA=OC (半径相等), 所以∠CAO = ∠ACO。 (Because OA=OC (radii are equal), therefore ∠CAO = ∠ACO). * 设∠ACO = x, 则: (Let ∠ACO = x, then:) * x + x + 124° = 180° * 2x + 124° = 180° * 2x = 56° * x = 28° 因此，∠ACO的度数为28°。答案是B。 (Therefore, the measure of ∠ACO is 28°. The answer is B.) ### Key Observations * The problem leverages fundamental geometric principles: the property of angles inscribed in a semicircle (90°), the relationship between central and inscribed angles, and the properties of isosceles triangles (equal sides imply equal angles). * The solution is presented in a clear, step-by-step manner. * The final answer is 28°, corresponding to option B. ### Interpretation The problem demonstrates a typical application of geometric theorems to solve for unknown angles within a circle. The solution methodically applies the given information and established rules to deduce the value of ∠ACO. The use of the inscribed angle theorem and the properties of isosceles triangles are crucial to the solution. The problem is well-structured and provides a clear path to the correct answer. The inclusion of multiple-choice options suggests this is likely a practice question or part of an assessment. The problem is designed to test understanding of basic geometric concepts and problem-solving skills. The diagram is a visual aid to help understand the relationships between the angles and segments. The Chinese text provides a complete and detailed explanation of the solution process.