CIRCUMSCRIBED

Circumscribed

Definition Of Circumscribed

A geometric figure that is drawn around another geometric figure so as to touch all its vertices is called Circumscribed.

More About Circumscribed

There are three different cases when a figure is circumscribed around another geometric figure:
Case 1: When a polygon is circumscribed around a circle
examples of Circumscribed

Triangle is circumscribed around a circle.
Case 2: When a circle is circumscribed around a polygon.
examples of Circumscribed

Video Examples: Circumscribed Circle

Circle is circumscribed around a triangle.
Case 3: When a polygon is circumscribed around another polygon
examples of Circumscribed

Quadrilateral is circumscribed around another quadrilateral.

Example of Circumscribed

examples of Circumscribed

In the figure given above, a circle is circumscribed around a triangle as all the vertices of the triangle lie on the circle

Solved Example onCircumscribed

Ques: Identify the circumscribed circle.

example of Circumscribed

Choices:

A. Figure 1
B. Figure 2
C. Figure 3
D. Figure 4
Correct Answer: C

Solution:

Step 1: A geometric figure that is drawn around another geometric figure so as to touch all its vertices is called Circumscribed.
Step 2: A circle is circumscribed about a polygon in such a way that all vertices of the polygon lie on the circle.
Step 3: Here, Figure 1 is a polygon circumscribed by another polygon.
Step 4: In Figure 2, one of the vertices of the polygon (triangle) is not touching the circle.
Step 5: Figure 3 has a polygon inside the circle. So, Figure 3 has a circle circumscribed around a polygon (square).
Step 6: Figure 4 has a circle inside a square. So, Figure 4 has a polygon circumscribed around a circle.
Step 7: So, Figure 3 is the circumscribed circle.

Quick Summary

A figure is circumscribed around another when it encloses the other and touches all its vertices.
Common cases include a polygon circumscribed around a circle, a circle circumscribed around a polygon, and a polygon circumscribed around another polygon.

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⚠️ Common Mistakes

Confusing circumscribed with inscribed (where the figure is inside and touches the sides).
Assuming that any figure enclosing another is circumscribed; all vertices must touch.

🌍 Real-World Uses

Designing packaging where a circular object (e.g., a can) must fit snugly inside a polygon-shaped box.
Architecture: Constructing a dome such that its base perfectly contains a polygonal structure.
Manufacturing lenses: Ensuring a lens (circle) is properly sized to fit a camera's rectangular housing.

📋 Standards Alignment

CCSS.MATH.CONTENT.HSG.CO.A.1
CCSS.MATH.CONTENT.HSG.CO.C.10

🍎 Teacher Insights

Use visual aids and hands-on activities to demonstrate the concept of circumscribed figures. Emphasize the importance of vertices touching the outer figure.

🎓 Prerequisites

Basic geometric shapes (circles, triangles, quadrilaterals, polygons)
Vertices
Tangency

Check Your Knowledge

Q1: Which of the following describes a circumscribed figure?

A. A figure inside another figure. B. A figure drawn around another touching all its sides. C. A figure drawn around another touching all its vertices. D. A figure tangent to another figure.

Q2: In a circumscribed circle, where do the vertices of the enclosed polygon lie?

A. Inside the circle. B. On the circumference of the circle. C. Outside the circle. D. At the center of the circle.

Frequently Asked Questions

Q: What is the difference between circumscribed and inscribed?
A: Circumscribed means drawn around a figure touching its vertices, while inscribed means drawn inside a figure touching its sides.

Q: Can a square be circumscribed around a circle?
A: Yes, if the circle is tangent to all four sides of the square.