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

# 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.*

## 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

## Tangent-Secant Theorem

Using the Tangent-Chord Theorem, it is simple to prove the third theorem which provides a relationship between lines in circles - the Tangent-Secant Theorem (the other two being the Intersecting … [Read more...] about Tangent-Secant Theorem

## The Tangent-Chord Theorem

The Tangent-Chord Theorem states that the angle formed between a chord and a tangent line to a circle is equal to the inscribed angle on the other side of the chord: ∠BAD ≅ … [Read more...] about The Tangent-Chord Theorem

## Intersecting Secants Theorem

A secant is a line that extends from a point outside the circle and goes through the circle. It intersects the circle at two points, and the line segment between those two points inside the circle is … [Read more...] about Intersecting Secants Theorem