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## 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.