Two circles that have the same center point are called concentric circles. A secant is a line that interest a circle (or any other curved line) at two or more point. We will now show that a secant … [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.
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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. Problem Circles 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
In today's lesson, we will show that a line connecting the centers of two intersecting circles is a perpendicular bisector of the common chord of the two circles, connecting the intersection … [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
In today's lesson, we will present a detailed, step-by-step proof of the Intersecting Secants Theorem, using properties of similar triangles. This is a fairly simple proof, so today's lesson will be … [Read more...] about Intersecting Secants Theorem
Congruent Chords are Equidistant from the Center
Chords that have an equal length are called congruent chords. An interesting property of such chords is that regardless of their position in the circle, they are all an equal distance from the … [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 diameter bisects two chords in a circle, the two chords are parallel to each other. We can do this this three ways, relying on the properties of … [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. Here, we will prove the converse theorem. Problem In circle O, the diameter AB is perpendicular to a chord CD. … [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. In today's lesson, we will first prove that a diameter that bisects a chord is perpendicular to that chord and … [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*PD Problem Prove that … [Read more...] about Intersecting Chords Theorem