**polygon inscribed in a circle**is said to be a cyclic

**polygon**, and the

**circle**is said to be its circumscribed

**circle**or circumcircle. The inradius or filling radius of a given outer figure is the radius of the

**inscribed circle**or sphere, if it exists.

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Keeping this in view, what does it mean for a polygon to be inscribed in a circle?

An **inscribed circle is** the largest possible **circle** that **can** be drawn on the **inside** of a plane figure. For a **polygon**, each side of the **polygon** must be tangent to the **circle**. All triangles and regular **polygons** have circumscribed and **inscribed circles**.

Secondly, is a circle a polygon? **Polygons**. A **polygon** is a closed plane figure with three or more sides that are all straight. A **circle** is not a **polygon** as it does not have straight sides.

Subsequently, one may also ask, what does it mean when a shape is inscribed?

**Inscribed**. The word is derived from the Latin “scribere” – to write or draw. It **means** to draw something inside something else. In geometry it usually **means** drawing one **shape** inside another so that it just touches. For example, the **figure** above is a circle **inscribed** in a triangle.

What is a Circumradius?

**Circumradius**. The **circumradius** of a regular polygon or triangle is the radius of the circumcircle, which is the circle that passes through all the vertices. See Circumcircle definition.

###
What is a circle inside a triangle called?

**inscribed circle**of a

**triangle**is the largest

**circle**contained in the

**triangle**; it touches (is tangent to) the three sides. The center of the incircle is a

**triangle**center

**called**the

**triangle’s**incenter.

###
Can a rectangle always be inscribed in a circle?

**rectangle can**be

**inscribed**in a (unique

**circle**) so the key point is that the radius of the

**circle**is R (I think). One of the properties of a

**rectangle**is that the diagonals bisect in the ‘center’ of the

**rectangle**, which

**will**also be the center of the circumscribing

**circle**.

###
How do you tell if a circle can be circumscribed?

**If**you’re given a convex quadrilateral, a

**circle can be circumscribed**about it

**if**and only the quadrilateral is cyclic. A nice fact about cyclic quadrilaterals is that their opposite angles are supplementary.

###
Can any regular polygon be inscribed in a circle?

**Every regular polygon**has an

**inscribed circle**(called its incircle), and

**every circle can**be

**inscribed**in

**some regular polygon**of n sides, for

**any**n≥3. Not

**every polygon**with more than three sides is an

**inscribed polygon**of a

**circle**; those

**polygons**that are so

**inscribed**are called cyclic

**polygons**.

###
What do you mean by circumscribing?

**Circumscribed**literally

**means**“to draw around”. A

**circumscribed**circle of a triangle for example is the circle that passes through all three vertices. Usually called the circumcircle.

###
What is the meaning of inscribed and circumscribed?

**inscribed**figure is a shape drawn inside another shape. A

**circumscribed**figure is a shape drawn outside another shape. For a polygon to be

**inscribed**inside a circle, all of its corners, also known as vertices, must touch the circle.

###
How do you find area?

**find the area**of a rectangle multiply its height by its width. For a square you only need to

**find**the length of one of the sides (as each side is the same length) and then multiply this by itself to

**find the area**. This is the same as saying length

^{2}or length squared.

###
How do you find out the area of a polygon?

**find**the

**area**of a regular

**polygon**, all you have to do is follow this simple formula:

**area**= 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the

**polygon’s**center to the midpoint of any side that is perpendicular to that side.

###
Is the Apothem equal to the side?

**apothem**refers to the length of the line the connects the center of a regular polygon to the midpoint of any of the

**sides**. A regular polygon has all congruent

**sides**; if the polygon is irregular, there is not a midpoint equidistant from the midpoint of all

**sides**. You can calculate the

**apothem**if you know the area.

###
How do you find the Apothem?

**find**the

**apothem**if we know both the area and perimeter of a polygon. This is because we can solve for a in the formula, A = (1/2)aP, by multiplying both sides by 2 and dividing by P to get 2A / P = a. Here, the

**apothem**has a length of 4.817 units.

###
Is a triangle a regular polygon?

**regular polygon**is a

**polygon**where all of the sides and angles are the same. An equilateral

**triangle**is a

**regular polygon**. It has all the same sides and the same angles. An isosceles

**triangle**has two equal sides and two equal angles.

###
What is area of a circle?

**Area of a circle**. The

**area of a circle**is pi times the radius squared (A = π r²). Learn how to use this formula to find the

**area of a circle**when given the diameter.

###
What is the opposite of inscribe?

**inscribe**. Antonyms: erase, efface, cancel, obliterate, expunge. Synonyms: letter, write, label, designate, delineate, mark, imprint, engrave, dedicate, address.

###
What does a polygon look like?

**polygon**is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of

**polygons**. The name tells you how many sides the shape has. For example, a triangle has three sides, and a quadrilateral has four sides.

###
Does a circle have sides?

**circle does**not

**have sides**. A “

**side**” usually refers to the

**sides**of a polygon, such as a square or a triangle.

###
How many triangles do you see?

**24 triangles**are located in the figure.