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This video can run circles around other videos about circles. Sir Cumference, of Round Table fame, explains all the properties of… well, circles....
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SAT Math 5.4 Geometry and Measurement 235 Views
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Description:
SAT Math 5.4 Geometry and Measurement
Transcript
- 00:03
Here’s your shmoop du jour, brought to you by chords.
- 00:06
Let’s make sweet, sweet music together.
- 00:09
The diameter of this circle is 14.
- 00:12
Lines JN and MK are perpendicular to each other. What is the length of the chord JK?
- 00:20
And here are the potential answers...
Full Transcript
- 00:25
We’re not sure where this circle is headed, but given the bow tie, it must be someplace fancy.
- 00:31
Okay, so this problem makes a big deal out of the fact that JN and MK are perpendicular…
- 00:36
What do the lines’ perpendicularity tell us?
- 00:38
It tells us that, because L is the midpoint of the circle…
- 00:41
…angle JLK is, by rule, a right angle.
- 00:45
The diameter of the circle is 14, which makes each radius 7…
- 00:48
…so we now also know the length of both JL and KL.
- 00:52
And whaddya know…by looking at our clock, it appears to be Pythagorean theorem time again…
- 00:58
Our “a” and “b” are each 7…
- 01:01
So when we take a squared plus b squared equals c squared…
- 01:04
…we get 7 squared plus 7 squared equals c squared…
- 01:09
49 plus 49 is 98…and the square root of 98 can simplify to 49 times 2…
- 01:15
…or 7 square root of 2.
- 01:17
Answer D.
- 01:18
There’s actually another way we could have gone about things…
- 01:21
We know that JKL is an isosceles triangle, given that it’s a right triangle and the
- 01:26
length of both sides is equal.
- 01:28
So we could have just used what we know about the ratio of sides in an isosceles triangle
- 01:33
to tell us that the hypotenuse must be x square root of 2…
- 01:37
…or, in this case, 7 square root of 2. Either way. It’s answer D.
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