Math Problem Statement
The image shows a geometric problem involving a semicircle and triangles. The questions are: 1) What type of triangle is △OAB? 2) What is the measure of the central angle labeled ⑦?
Solution
The image shows a geometric problem involving a semicircle and triangles. Let's analyze the content and answer the questions.
Problem Analysis:
- 問1: What type of triangle is △OAB?
- 問2: What is the measure of the central angle labeled ⑦?
Solution:
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問1 (Type of △OAB):
- The figure shows a semicircle with diameter . Triangle is inscribed in the semicircle with as its hypotenuse.
- By the Inscribed Angle Theorem, any triangle inscribed in a semicircle with the diameter as one side is a right triangle.
- Therefore, △OAB is a right triangle with a right angle at point .
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問2 (Measure of the central angle labeled ⑦):
- Central angle ⑦ is subtended by arc of the semicircle. In a semicircle, the central angle that subtends the entire diameter is always . However, since this question specifically refers to angle ⑦, which likely subtends only a segment of the semicircle:
- The measure of angle ⑦ depends on the specific configuration shown. Without precise measurements, it's challenging to provide an exact degree, but the information suggests it is proportional to the arc's length that angle ⑦ subtends.
Would you like more details on the central angle calculation, or do you have any other questions?
Related Questions:
- How do you determine the type of a triangle inscribed in a semicircle?
- What is the Inscribed Angle Theorem, and how does it apply to triangles in a semicircle?
- How do you calculate central angles in circles when given arcs?
- What properties do right triangles have when inscribed in semicircles?
- Can the measure of angle ⑦ be determined exactly without additional data?
Tip: Always remember that a triangle with one side as the diameter of a semicircle is a right triangle, a key property of semicircle inscribed figures.
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Math Problem Analysis
Mathematical Concepts
Geometry
Triangles
Semicircles
Angles
Formulas
Inscribed Angle Theorem
Central Angle Formula
Theorems
Inscribed Angle Theorem
Right Triangle Property in a Semicircle
Suitable Grade Level
Grades 8-10