WEBVTT
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So we're back with Maura about circles and the special
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angles that are formed and how toe measure or calculate
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those angles. Now, when I say special angles
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, I mean special angles formed by certain line segments
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that cross through the circle. So a few background
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concepts first, here's your circle. Recall that if
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you have a circle and you have a segment that
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has it's end points on the circle, we call
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this accord and that you can have minor chords,
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which is this type of cord or major chord,
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which is a line say, when that goes through
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the center. Both of these records, however,
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the one I'm pointing out is a minor chord,
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the one that goes to the diameter. That part
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of me that the one that is the diameter that
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goes to the center of the circle is called a
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major chord. Well, sometimes you can have cords
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cross like so, but not go through the center
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so we would know how to find the measure of
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angles and arcs If we knew that they went through
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the center nicely because we could use the rules for
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how to find the measurements of a central angle or
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inscribed angle. That's not the case if our cords
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cross it, a point that is not the center
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. So now we have some angles in the interior
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of the circle that don't abide by those two rules
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. So here's a couple of themes for these unique
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angle situations. If you have two cords crossing,
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then the angle formed by the two intersecting lines is
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going to be half of the some of the two
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arcs that they sub tend. So this arc plus
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this arc divided by two, will equal the angle
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in question. So an example would be like this
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. Here's a circle. Here's my center, but
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here's my two chords. Let's say I knew that
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this ark was 20 degrees in this arc was 60
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degrees completely making this up. Therefore, this angle
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here is going to be half the sum of the
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two arcs That's gonna be half of 80 or,
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in other words, 40 degrees. So this angle
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here would equal 40 degrees. Okay, that's one
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of three therms. I'm gonna show you. Okay
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, if we had something very similar to that,
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but we had the Okay, the cords extend from
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the circle. Pardon me. So let's say we
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had this going on now. First of all,
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what I'm drawing in green. That's accord. That's
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accord if you extend it and look at the bigger
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picture. Really, What we're dealing with is these
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lines called sequence. Both of these are known as
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sequence S E C. A N T sequence sequence
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are lines. Raise land segments that cross a circle
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twice, so notice that each of these rays is
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crossing the circle twice. Now what you get is
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an angle on the exterior of the circle. But
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that angle, like the previous example sub, tends
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to works of the circle. This time, the
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angle in question is going to be one half the
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difference of the two. So let's say this were
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80 and this were 20 degrees, and we were
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given. Those arcs are 80 and 20 degrees,
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respectively. Then the angle excess in question would be
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one half, and then it would be 80.
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Pardon me, minus 20 which would be one half
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of 60 or, in other words, 30 degrees
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. So if the angle were formed by two chords
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or sequence with inside of the circle, then the
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angle is going to be essentially the average of the
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two arcs that its substance one R plus the other
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arc divided by two. If the angle is formed
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in the outside of the circle, as you can
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see here, then the angle is going to be
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equal to the half of the difference of the two
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. Okay, now it's time to introduce one new
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type of segment. We'll get to know a lot
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more in a few lessons from now. But if
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you have a circle and you have a line that
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goes in a liner, a line segment or array
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that just touches the circle, do a little better
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just touches the circle on exactly one point. This
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segment is known as a tangent, so it's possible
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that we could have something like this where we have
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one second and we have one tangent and we have
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this angle here. So if we wanted to figure
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out the Rule two number for how to find this
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angle, X, let me draw that in different
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color. Then, once again like the previous example
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, it's going to be one half this ark minus
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disorder. Yeah, because we still have an angle
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that sub tending two different arcs of the circle.
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But there's a very special situation. What if we
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had a circle? Here's the center we had a
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tangent, but this time the angle came from what
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we call the point of tangent C that is called
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the point of Tangent C. What is this angle
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then? Well, since it on Lee sub tends
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one arc, technically, it sometimes, too.
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But one of them is zero. So instead of
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having one arc minus the other divided by two,
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So instead of finding half the difference you technically are
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, it's just the one arc zero because it only
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sub tends technically this particular arc. So let's say
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I knew that this arc here were 100 degrees thin
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. This angle in question is gonna be one half
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of 100 or, in other words, 50.
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So those were three additional angle the're ums or not
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doing the formal proofs by any means. But those
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air three additional rules that pertain to angles inside,
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outside and technically sort of on the circle, depending
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on how the sequence and tangents air interacting with each
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other is there different than the central and inscribed angle
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rules because we're not coming from the center, Nor
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are we coming from directly on the circle. Mawr
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examples coming soon