9.4 - Angle Subtended by an Arc of a Circle
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Practice Questions
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If chord AB = chord CD in a circle, what can you say about arcs AB and CD?
💡 Hint: Think about the relationship between equal chords and their corresponding arcs.
What is the measure of an angle subtended by the chord at a point on the circle if it is 30 degrees at the center?
💡 Hint: Remember that the angle at the center is double the angle at the circumference.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is true about chords that subtend equal angles at the center of a circle?
💡 Hint: Consider the relationship between the arc and chord lengths.
True or False: The angle at the center is always greater than the angle at any point on the circumference.
💡 Hint: Reflect on the theorems we discussed related to arcs.
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Challenge Problems
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Two points A and B are on the circumference, and they subtend an angle of 100° at point C, which is on the circle. If point D is the center of the circle, what angle does ∠ ADB equal?
💡 Hint: Use the relationship established by Theorem 9.7.
Prove that if two angles subtend equal arcs in the same circle, the segments formed by those arcs must also equal in size.
💡 Hint: Think about inscribed and central angles together.
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