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
Chords
A chord is a straight line connecting two points on the circle.
The diameter is a special chord, which passed through the center of the circle, and its length is 2*r. It is the longest possible chord in the circle.
--
Now that we've explained the basic concept of chords in geometry, let's scroll down to work on specific geometry problems relating to this topic.
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
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
Congruent Chords are Equidistant from the Center
Chords that have an equal length are called congruent. An interesting property of such chords is that regardless of their position in the circle, they are all an equal distance from the circle's … [Read more...] about Congruent Chords are Equidistant from the Center
A Diameter that bisects two chords
In today's geometry lesson, we will prove that if a dimeter bisects two chords, they are parallel to each other.ProblemIn circle O, a diameter, AB, bisects two chords, CD and EF. Show that … [Read more...] about A Diameter that bisects two chords
A Diameter Perpendicular to a Chord
We've shown that a diameter that bisects a chord is perpendicular to that chord. Now let's prove the opposite: that a diameter that is perpendicular to a chord bisects that chord.ProblemIn the … [Read more...] about A Diameter Perpendicular to a Chord
A Diameter Bisecting a Chord
There are several theorems related to chords and radii or diameters that connect to them. We will first prove that a diameter that bisects a chord is perpendicular to that chord, and bisects the arc … [Read more...] about A Diameter Bisecting a Chord
Intersecting Chords Theorem
The intersecting chords theorem states that when two chords intersect at a point, P, the product of their respective partial segments is equal.In other words: AP*PB=CP*PDProblemProve that … [Read more...] about Intersecting Chords Theorem