A tangential quadrilateral is a quadrilateral whose four sides are all tangent to a circle inscribed within it. In such a quadrilateral, the sum of lengths of the two opposite sides of the … [Read more...] about Circle Inscribed in a Quadrilateral

# Inscribed Shapes

Many geometry problems deal with shapes inside other shapes. For example, circles within triangles or squares within circles.

The inner shape is called "inscribed," and the outer shape is called "circumscribed."

When a circle is inscribed inside a polygon, the edges of the polygon are tangent to the circle.

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*Now that we've explained the basic concept of inscribed shapes in geometry, let's scroll down to work on specific geometry problems relating to this topic.*

## A Circle Inscribed in a Square

We've seen that when a square is inscribed in a circle, we can express all the properties of either the square or circle (area, perimeter, circumference, radius, side length) if we know just the … [Read more...] about A Circle Inscribed in a Square

## Square Inscribed in a Circle

When a square is inscribed in a circle, we can derive formulas for all its properties- length of sides, perimeter, area and length of diagonals, using just the circle's radius. Conversely, we can … [Read more...] about Square Inscribed in a Circle

## Kite Inscribed in a Circle

When we inscribe a kite is in a circle, all four of the kite's vertices lie on the circle's circumference. In today's lesson, we will show that in the case of a kite inscribed in a circle, the axis … [Read more...] about Kite Inscribed in a Circle

## Circumscribed Circle

In geometry, "circumscribed" means "to draw around." A circumscribed circle is a circle that is drawn around a polygon so that it passes through all the vertices of a polygon inscribed in it. All … [Read more...] about Circumscribed Circle

## Area of a Circle Inscribed in an Equilateral Triangle

We can use the properties of an equilateral triangle and a 30-60-90 right triangle to find the area of a circle inscribed in an equilateral triangle, using only the triangle's side … [Read more...] about Area of a Circle Inscribed in an Equilateral Triangle

## Radius of a Circle with an Inscribed Triangle

In today's lesson, we will learn how to find the radius of a circle with an inscribed triangle. Many geometry problems involve a triangle inscribed in a circle, where the key to solving the … [Read more...] about Radius of a Circle with an Inscribed Triangle

## Inscribed Shapes: Opposing Angles of a Quadrangle Inscribed in a Circle

In today's lesson, we will prove that in a quadrangle inscribed in a circle, the opposing angles are supplementary. Not all quadrangles can be inscribed in a circle. Intuitively, if we think of a … [Read more...] about Inscribed Shapes: Opposing Angles of a Quadrangle Inscribed in a Circle

## Polygon Inscribed in a Circle

We will solve most problems involving polygons inscribed in a circle by using theorems related to inscribed angles, as the vertices of the polygons form inscribed angles. Problem An irregular … [Read more...] about Polygon Inscribed in a Circle