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.

Example of Inscribed 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 on Inscribed Polygon

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: ΔABD, ΔBCD, ΔADC, ΔABC and quadrilateral ABCD are the only inscribed polygons.
Step 3: ΔAOD, ΔDOC, ΔOCB and ΔAOB 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.

Related Terms for Inscribed Polygon

  • Chord
  • Circle
  • Vertex