INSCRIBED POLYGON
Definition Of Inscribed Polygon
Inscribed Polygon is defined as a polygon placed inside a circle so that all the vertices of the polygon lie on the circumference of the circle.
More About Inscribed Polygon
All the sides are chords in an inscribed polygon.
Video Examples: Inscribed Polygons
Example ofInscribed Polygon
In the given figure, the vertices A, B, and C of the triangle lie on the circumference of the circle. So, triangle ABC is an inscribed polygon.
Solved Example onInscribed Polygon
Ques: How many inscribed polygons are there in the figure?
Choices:
A. 6
B. 3
C. 4
D. 5
Correct Answer: D
Solution:
Step 1: A polygon is said to be inscribed in a circle if each of its sides is a chord.
Step 2: â–³ABD, â–³BCD, â–³ADC, â–³ABC and quadrilateral ABCD are the only inscribed polygons.
Step 3: â–³AOD, â–³DOC, â–³OCB and â–³AOB are not inscribed polygons, because all of their sides are not chords of the circle.
Step 4: So, 5 polygons are inscribed in the figure.
Quick Summary
- An inscribed polygon is contained within a circle.
- All vertices of the polygon lie on the circle's circumference.
- The sides of the inscribed polygon are chords of the circle.
🍎 Teacher Insights
Use dynamic geometry software to allow students to explore different polygons and circles and visualize the concept of inscription. Emphasize the relationship between the polygon's vertices and the circle's circumference.🎓 Prerequisites
- Circles
- Polygons
- Chords
- Vertices
Check Your Knowledge
Q1: Which of the following is true about an inscribed polygon?
Q2: If a triangle is inscribed in a circle, its sides are ______ of the circle.
Frequently Asked Questions
Q: Are all polygons able to be inscribed in a circle?
A: No, only cyclic polygons (those whose vertices lie on a circle) can be inscribed.
Q: Is a square able to be inscribed in a circle?
A: Yes, a square can be inscribed in a circle.