Question

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

Answer 1

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)

Answer 2

Use Pythagorean Theorem to find length of chord AB

Answer 3

i dont know how..

Answer 4

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?

Answer 5

no...

Answer 6

May I ask what grade you're in and what course you're working on?

Answer 7

im in 11 and in geometry but im doing online math this summer....

Answer 8

OK. You know what a right triangle is, right?

Answer 9

yes.

Answer 10

Can you identify which sides are the legs and which side is the hypotenuse?

Answer 11

i think so

Answer 12

OK. In the figure I drew, which side is the hypotenuse?

Answer 13

AB?

Answer 14

That's right.

Answer 15

So the other two sides are the legs. Both of these legs are \(r\) unit in length. Do you see where that comes from?

Answer 16

ya

Answer 17

Good.

Answer 18

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?

Answer 19

no u lost me

Answer 20

\(AB^2\) is the length of the hypotenuse squared. OK?

Answer 21

ok

Answer 22

\(AO^2\) is the length of one of the legs squared.
\(OB^2\) is the length of the other leg squared. OK?

Answer 23

ok

Answer 24

Is there an easier way of learning this?

Answer 25

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?

Answer 26

no not really.. Im really slow with math.. ive never been any good

Answer 27

If \[\left( AO \right) = r\]then \[\left( AO \right)^2 = r^2\]OK?

Answer 28

ok

Answer 29

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?

Answer 30

um kinda

Answer 31

Well if \[AO^2 = r^2\] and \[OB^2 = r^2\]then \[AO^2 + OB^2 = r^2 + r^2\]

Answer 32

okay

Answer 33

Now \[r^2 + r^2 = 2r^2\]You OK with that?

Answer 34

yas

Answer 35

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?

Answer 36

i dont think so

Answer 37

What is the square root of AB^2?

Answer 38

umm.. No clue. Im going into all this blind

Answer 39

What is the square root of any number squared? If 2^2 = 4, what is the square root of 4?

Answer 40

2??

Answer 41

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?

Answer 42

ohhh okay

Answer 43

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?

Answer 44

umm i have no clue

Answer 45

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\[AB = r \sqrt{2}\]

Answer 46

ohhh okay thank u soo much

Answer 47

You're welcome.

Answer 48

thats what i had too!!!!