When we have two chords that crossing inside a circle, as presented below, the two triangles that result are similar.
You are watching: A circle with two chords is shown below
This renders the matching sides in each triangle proportional and leads to a relationship between the segment of the chords, as proclaimed in the Intersecting Chords Theorem.
Intersecting Chords Theorem: If two chords intersect inside a one so that one is separated into segment of length a and also b and the other into segments of length \\(c\\) and also \\(d\\) climate \\(ab=cd\\).
Use the Intersecting Chords Theorem.
\\(15\\cdot 4=5\\cdot x\\)
Find \\(x\\). Simplify any kind of radicals.
Solutionuse the Intersecting Chords Theorem.
\\(\\beginaligned 8\\cdot 24&=(3x+1)\\cdot 12 \\\\192&=36x+12 \\\\ 180&=36x \\\\ 5&=x\\endaligned\\)use the Intersecting Chords Theorem.
\\(\\beginaligned (x−5)21&=(x−9)24 \\\\ 21x−105&=24x \\\\ 111&=3x \\\\ 37−216&=x \\endaligned\\)
|central angle||An angle formed by two radii and also whose vertex is in ~ the center of the circle.|
|chord||A heat segment who endpoints are on a circle.|
|circle||The collection of every points that space the exact same distance far from a particular point, called the center.|
|diameter||A chord the passes through the facility of the circle. The length of a diameter is 2 times the size of a radius.|
|inscribed angle||An angle v its crest on the circle and whose sides room chords.|
|intercepted arc||The arc that is within an inscriptions angle and also whose endpoints space on the angle.|
|radius||The street from the center to the external rim that a circle. |
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|Intersecting Chords Theorem||According to the Intersecting Chords Theorem, if 2 chords intersect inside a one so that one is divided into segment of length \\(a\\) and also \\(b\\) and the other into segments of length \\(c\\) and also \\(d\\), climate \\(ab = cd\\).|