INSCRIBED ANGLE
Definition Of Inscribed Angle
Inscribed Angle is defined as the angle formed by two chords that meet at the same point on a circle.
More About Inscribed Angle
The measure of an inscribed angle is half the measure of the central angle formed by using the same end points.
Video Examples: Geometry - Inscribed Angles
Example of Inscribed Angle
In the figure, AB and BC are two chords which meet at point B on the circle. So, ∠ABC is an inscribed angle.
Solved Example on Inscribed Angle
Ques: Identify an inscribed angle.
Choices:
A. ∠ABO
B. ∠BOC
C. ∠BAC
D. ∠OCA
Correct Answer: C
Solution:
Step 1: An inscribed angle is the angle formed by two chords of a circle that meet at the same point on the circle.
Step 2: Here, in the figure, ∠BAC is an inscribed angle as two chords BA and CA meet at point A.
Step 3: Therefore, ∠BAC is an inscribed angle in the given figure.
Quick Summary
- Inscribed angles are formed by two chords with a common endpoint on the circle.
- The measure of an inscribed angle is half the measure of its intercepted arc.
- Inscribed angles that intercept the same arc are congruent.
🍎 Teacher Insights
Use dynamic geometry software to allow students to explore the relationship between inscribed angles and central angles. Emphasize the importance of the vertex of the angle lying on the circumference.🎓 Prerequisites
- Circles
- Chords
- Angles
- Central Angles
Check Your Knowledge
Q1: In circle O, if inscribed angle ABC intercepts arc AC, and arc AC measures 80 degrees, what is the measure of angle ABC?
Q2: Which of the following is an inscribed angle?
Frequently Asked Questions
Q: What is the relationship between an inscribed angle and a central angle that intercepts the same arc?
A: The measure of the inscribed angle is half the measure of the central angle.
Q: Can an inscribed angle be a right angle?
A: Yes, if it intercepts a semicircle.