# What is a circumscribed circle?

In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.

Also asked, what is the difference between an inscribed and a circumscribed circle?

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. If any vertex fails to touch the circle, then it’s not an inscribed shape.

What is an inscribed polygon?

An inscribed polygon might refer to any polygon which is inscribed in a shape, especially: A cyclic polygon, which is inscribed in a circle (the circumscribed circle) A midpoint polygon of another polygon.

## What is the difference between an inscribed and a circumscribed circle?

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. If any vertex fails to touch the circle, then it’s not an inscribed shape.

## What is special about the Circumcenter?

The circumcenter is the center of a triangle’s circumcircle. It can be found as the intersection of the perpendicular bisectors.

## What is the circumscribed circle of a triangle?

The circumcircle of a triangle is the circle that passes through all three vertices of the triangle. The construction first establishes the circumcenter and then draws the circle. circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect.

## What is inscribed and circumscribed?

The center of this circle is called the circumcenter. 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.

## Which is the best definition of a circle?

Definition: A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. We use the symbol ⊙ to represent a circle. The a line segment from the center of the circle to any point on the circle is a radius of the circle. An arc is a connected portion of a circle.

## What do you mean by circumscribed?

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 circumscribed of a triangle?

A circle that circumscribes a triangle is a circle containing the triangle such that the vertices of the triangle are on the circle. A circle that inscribes a triangle is a circle contained in the triangle that just touches the sides of the triangle.

## What is the Circumcenter in geometry?

Circumcenter. Usually applies to a triangle, but also to regular polygons. The point where the three perpendicular bisectors of the sides of a triangle meet. Also, the center of the circumcircle. One of a triangle’s points of concurrency.

## How do you circumscribe a circle around a triangle?

Construct the perpendicular bisector of one side of triangle. Construct the perpendicular bisector of another side. Where they cross is the center of the Circumscribed circle. Place compass on the center point, adjust its length to reach any corner of the triangle, and draw your Circumscribed circle!

## What is a circumscribed angle?

Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

## What is a major arc in math?

A major arc (right figure) is an arc of a circle having measure greater than or equal to ( radians). SEE ALSO: Arc, Minor Arc, Semicircle.

## Can a circle be inscribed in a circle?

A 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.

## What is meant by concentric circles?

Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus. Any two circles can be made concentric by inversion by picking the inversion center as one of the limiting points.

## Why is the Incenter called the Incenter?

Note the way the three angle bisectors always meet at the incenter. One of several centers the triangle can have, the incenter is the point where the angle bisectors intersect. The incenter is also the center of the triangle’s incircle – the largest circle that will fit inside the triangle.

## What is the Orthocentre?

The orthocenter is the point where all three altitudes of the triangle intersect. An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side. There are therefore three altitudes in a triangle.

## How do you inscribe a circle in a triangle?

Inscribe a Circle in a Triangle

• Bisect one of the angles.
• Bisect another angle.
• Where they cross is the center of the inscribed circle.
• Construct a perpendicular from the center point to one side of the triangle.
• Place compass on the center point, adjust its length to where the perpendicular crosses the triangle, and draw your inscribed circle!
• ## What is the intercepted arc of a circle?

The intercepted arc is a section of the circumference of a circle. It is encased on either side by two different chords or line segments that meet at one point, called a vertex, on the other side of the circle or in the middle of the circle.

## What is an Escribed circle?

An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle’s sides.

## What is the difference between a right acute and obtuse triangle?

An acute triangle is a triangle with all three angles acute (less than 90°). An obtuse triangle is one with one obtuse angle (greater than 90°) and two acute angles. Since a triangle’s angles must sum to 180°, no triangle can have more than one obtuse angle.

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