Two chords that make an inscribed angle.
A. are perpendicular
B. share an endpoint
C. bisect each other
D. are parallel
Answer (2)
An inscribed angle is formed by two chords in a circle.
The defining characteristic of an inscribed angle is that the two chords share a common endpoint.
Other options like perpendicularity, bisection, or parallelism are not necessary conditions.
Therefore, the two chords must share an endpoint: B .
Explanation
Analyze the problem and options. An inscribed angle is formed by two chords in a circle that share a common endpoint. Let's analyze each option:
A. are perpendicular: Chords forming an inscribed angle do not necessarily have to be perpendicular. They can form any angle.
B. share an endpoint: This is the definition of an inscribed angle. The two chords must share an endpoint on the circle.
C. bisect each other: Chords that bisect each other create specific geometric relationships, but this is not a requirement for forming an inscribed angle.
D. are parallel: Parallel chords do not form an angle; they run in the same direction.
Therefore, the correct answer is that the two chords must share an endpoint.
State the final answer. The two chords that make an inscribed angle must share an endpoint.
Examples
In architecture, when designing arched windows or doorways, understanding inscribed angles helps ensure structural integrity and aesthetic appeal. The chords forming the arch must meet at a common point on the circle to create a smooth, visually pleasing curve. This principle also applies in bridge design, where curved supports rely on the geometry of circles and inscribed angles to distribute weight evenly.
The two chords that form an inscribed angle must share a common endpoint. This is the defining property of inscribed angles. Therefore, the correct answer is option B.
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