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
Triangle is circumscribed around a circle.
Case 2: When a circle is circumscribed around a polygon.
Video Examples: Circumscribed Circle
Circle is circumscribed around a triangle.
Case 3: When a polygon is circumscribed around another polygon
Quadrilateral is circumscribed around another quadrilateral.
Example 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.
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.