anonymous
  • anonymous
Will medal and fan Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the length of the chord whose endpoints are the points of tangency. 2r r² r√2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
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anonymous
  • anonymous
Find the coordinates of the other endpoint if the midpoint is M(8, 2) and the other endpoint is P(5, 6). (6.5, 4) (21, 10) (11, -2)
anonymous
  • anonymous
|dw:1439227683307:dw| Use Pythagorean Theorem to find length of chord AB

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anonymous
  • anonymous
i dont know how..
anonymous
  • anonymous
Triangle AOB is a right triangle. The lengths of the sides are related byt the Pythagorean Theorem. If a right triangle has legs of lengths a and b, and a hypotenuse of length c, these lengths are related by\[a^2 + b^2 = c^2\]Have you seen this before?
anonymous
  • anonymous
no...
anonymous
  • anonymous
May I ask what grade you're in and what course you're working on?
anonymous
  • anonymous
im in 11 and in geometry but im doing online math this summer....
anonymous
  • anonymous
OK. You know what a right triangle is, right?
anonymous
  • anonymous
yes.
anonymous
  • anonymous
Can you identify which sides are the legs and which side is the hypotenuse?
anonymous
  • anonymous
i think so
anonymous
  • anonymous
OK. In the figure I drew, which side is the hypotenuse?
anonymous
  • anonymous
AB?
anonymous
  • anonymous
That's right.
anonymous
  • anonymous
So the other two sides are the legs. Both of these legs are \(r\) unit in length. Do you see where that comes from?
anonymous
  • anonymous
ya
anonymous
  • anonymous
Good.
anonymous
  • anonymous
The Pythagorean Theorem says that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. In our diagram\[\left( AB \right)^2 = \left( AO \right)^2 + \left( OB \right)^2\]Do you understand so far?
anonymous
  • anonymous
no u lost me
anonymous
  • anonymous
\(AB^2\) is the length of the hypotenuse squared. OK?
anonymous
  • anonymous
ok
anonymous
  • anonymous
\(AO^2\) is the length of one of the legs squared. \(OB^2\) is the length of the other leg squared. OK?
anonymous
  • anonymous
ok
anonymous
  • anonymous
Is there an easier way of learning this?
anonymous
  • anonymous
Now, for any right triangle, the lengths of the sides are related, no matter the size. The relationship is, as stated earlier\[\left( AB \right)^2 = \left( AO \right)^2 + \left( OB \right)^2\]Now, we know that the lengths of the legs (AO & OB) are equal to \(r\). So, substituting that value in, we get\[\left( AB \right)^2 = r^2 + r^2 = 2r^2\]Understand?
anonymous
  • anonymous
no not really.. Im really slow with math.. ive never been any good
anonymous
  • anonymous
If \[\left( AO \right) = r\]then \[\left( AO \right)^2 = r^2\]OK?
anonymous
  • anonymous
ok
anonymous
  • anonymous
And if \[\left( OB \right) =r\]then\[\left( OB \right)^2 = r^2\]Then by adding them together\[\left( AB \right)^2 + \left( OB \right)^2 = r^2 + r^2\]Still with me?
anonymous
  • anonymous
um kinda
anonymous
  • anonymous
Well if \[AO^2 = r^2\] and \[OB^2 = r^2\]then \[AO^2 + OB^2 = r^2 + r^2\]
anonymous
  • anonymous
okay
anonymous
  • anonymous
Now \[r^2 + r^2 = 2r^2\]You OK with that?
anonymous
  • anonymous
yas
anonymous
  • anonymous
Alright. Putting all of that together, we have\[AB^2 = AO^2 + OB^2\]\[AB^2 = r^2 + r^2\]\[AB^2 = 2r^2\]Now the question requires that we solve for AB. To do that, you need to take the square root of both sides. Can you do that?
anonymous
  • anonymous
i dont think so
anonymous
  • anonymous
What is the square root of AB^2?
anonymous
  • anonymous
umm.. No clue. Im going into all this blind
anonymous
  • anonymous
What is the square root of any number squared? If 2^2 = 4, what is the square root of 4?
anonymous
  • anonymous
2??
anonymous
  • anonymous
Right. And if 3^2 = 9, the square root of 9 is 3. So the square root of any number squared is that number. Now just do it with a variable instead of a number. So what is the square root of AB^2?
anonymous
  • anonymous
ohhh okay
anonymous
  • anonymous
So\[AB^2 = 2r^2\]\[\sqrt{AB^2} = \sqrt{2r^2}\]\[AB = \sqrt{2} \sqrt{r^2}\]And what is the square root of r^2?
anonymous
  • anonymous
umm i have no clue
anonymous
  • anonymous
We just covered it. The square root of any number squared is that same number. So the square root of r^2 is r. So your answer is\[AB = r \sqrt{2}\]
anonymous
  • anonymous
ohhh okay thank u soo much
anonymous
  • anonymous
You're welcome.
anonymous
  • anonymous
thats what i had too!!!!

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