![]() ![]() “Intercepted Arc – Explanation & Examples.” n.d.Indeed why? Why a diameter is the longest chord in a circle? I sometimes heard and several times read at popular math sites that the reason why a diameter is the longest chord is that a diameter passes through the center of the circle.“Intersecting Secant Angles Theorem – Math Open Reference.” n.d.I hope this video on secants, chords, and tangents was helpful! Thanks for watching, and happy studying! We can see that by zooming in on a circle that shows the angles that are just a few degrees away from 90°:Įven if the angle were even closer to 90°, such as 90.1° and 89.9° this would still happen, though it would be really hard to show on a diagram! This would actually create a secant instead of a tangent line. If our line isn’t exactly perpendicular to the radius at the point of tangency it will actually touch the circle twice, though possibly very close together. For our line to be truly tangent, this must be true. Here it means the line that is touching the circle in the slightest way possible – only at one point.Īnyway, looking closely at our diagram, we can see a radius of the circle meeting our tangential line at a 90° angle. We see the word tangential outside of math sometimes too, describing a topic that is only slightly related to the topic being discussed. The point where the line and the circle touch is called the point of tangency. If a line passes by a circle and only touches it in one point, it creates what we call a line that is a tangent to the circle. When a line and circle interact, sometimes secants aren’t created. Problems on the standardized tests are sometimes not drawn to scale – watch for a warning to that effect on any problem you do. If we accidentally used the addition formula, we would end up with an angle measuring 65°, which appears to be way too big for our little angle. We can do a little common sense check to make sure we’re using the right version of this formula. That means we can find our inscribed angle by dividing our central angle by two, which means our inscribed angle is \(120^\) That’s because it is! In fact, it’s exactly twice as wide. Notice how the central angle is quite a bit “wider” than our inscribed angle. The central angle measures 120°, so our intercepted arc also measures 120°. The intercepted arc is the same measure as the central angle that uses the same two points as our inscribed angle, but with its vertex at the center of the circle. We can find the measure of our inscribed angle \(x\) if we know the length of the intercepted arc in degrees. Across from the angle is the part of the circle between the points where the chords intersect the circle, highlighted in yellow. Now our two chords have created an inscribed angle in our circle, which we’ve labeled with an \(x\) and a degree symbol. We can also have more than one secant to the circle interacting with each other, like this: We can see that the line intersects the outside of the circle at two points and creates a line segment between those points, which is highlighted in red. A line cutting across a circle that touches two points on the outside of the circle is a secant to the circle. Let’s start by defining the vocabulary we’ll need. Hello! Today we’re going to explore what can happen when a circle and a line or two lines meet. ![]()
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