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

# Circles

In geometry, a circle is defined as the collection of all points that are the same distance from one point, which is the center of the circle.

The distance from the center of the circle to any point on the circle is called the radius, and commonly written 'r'.

If we draw a line from one point on the circle, through its center and on to another point on the circle, directly across from the first point, that line's length will be 2 times r, and is called the circle's diameter, 'd'. d= 2*r

A circle is a geometric shape completely defined by its radius- knowing the radius we can calculate the circle's area, and its circumference.

A circle's circumference, C, is C_{circle}=2*π*r (where r is the radius) , and since the diameter, d, is 2 times r, we can also write C_{circle}=d*π

A circle's area is given by the formula A_{circle}=π*r^{2}

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*Now that we've explained the basic concept of circles 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

## Thales’ Theorem

Thales of Miletus was a Greek mathematician who's work predates that of Euclid and Pythagoras.There are a number of theorems associated with his name -one is the Intercept Theorem for the ratios … [Read more...] about Thales’ Theorem

## Kite Inscribed in a Circle

If we inscribe a kite is in a circle (that is, all four of its vertices lie on the circle's circumference), then the axis of symmetry of the kite is the circle's diameter, as we will now … [Read more...] about Kite Inscribed in a Circle

## Concentric Circles Intersected by a Secant

Two circles that have the same center point are called concentric circles. A secant line that intersects both of the concentric circles creates two congruent segments between the two … [Read more...] about Concentric Circles Intersected by a Secant

## Finding the Length of a Common Chord

If we know the radii of two intersecting circles, and how far apart their centers are, we can calculate the length of the common chord.ProblemCircles O and Q intersect at points A and B. The … [Read more...] about Finding the Length of a Common Chord

## Common Chord of Two Circles

When two circles intersect, we can connect the two intersection points and create a common chord.If we connect the centers of these two circles, the connecting line will be a perpendicular … [Read more...] about Common Chord of Two Circles

## Distance Between the Centers of Overlapping Congruent Circles

Congruent circles have the same radius length.ProblemTwo congruent circles with radius 1 unit overlap, with the overlapping arc, AB, measuring π/3 units. Find the distance between the centers … [Read more...] about Distance Between the Centers of Overlapping Congruent Circles

## 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