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So let's discover some more circle theorems, so that we can solve all types of geometrical problems.
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We discovered these four theorems in part one.
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So if you aren't familiar with some of these, watch that video first.
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Before we start, you should know what all of these terms mean, if you aren't sure what that video first.
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So let's go discovering some more theorems, what do you notice about the angle between the tangent and the radius.
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Remember that a tangent is a line that touches a circle at only one point.
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So that's theorem five, the angle between a tangent and a radius is 90 degrees.
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What do you notice about the lengths of the tangents?
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The length of two tangents from a point to a circle are equal.
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This is useful to bear in mind, as it means you have two identical triangles.
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So, we've got tangents and radius give 90 degrees and we've got two tangents of the same length.
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There's just one final thing to learn about tangents and circles.
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Can you see what's happening with the angles?
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This theorem is known as the alternate segment theorem:
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the angle between a tangent and a chord it's equal to the angle in the alternate segment.
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I've always just thought of it as the angle that's furthest away, so it can't be this angle because it's next to it.
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And it can't be this angle because it's on the same line.
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So, that means it has to be this angle, the alternate segment theorem.
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So this one can be tricky to remember.
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Maybe you want to write it down somewhere that you see it a lot, like on the back of your bedroom door.
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So we've now covered nearly all of the theorems.
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All we have left to look at is the final two theorems to do with cords, which we'll see in part three.
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Can you remember all three theorems that we've looked at in this video?
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Pause the video, drop them down making sure you use the correct terminology and click play when you're ready to check.
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How did you get on?
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So, here are three questions for you to do.
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Question three requires you to use your knowledge off parallel line angles and isosceles triangles.
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Pause the video, find the missing angles and click play when you're ready to check.
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How did you do?
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So, there we have seven circle theorems.
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When you're on your way home from school or waiting in a queue, see how many you can remember.
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In part three, we're going to discover the final two theorems that have to do with intersecting chords.