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# help geometry

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What is MN?

Jul 1, 2021

### Best Answer

#1
+447
-1

Let P be the intersection point of MN and KL, and let x equal MP. You could use the intersecting chord theorem for this problem, but notice that the lines are perpendicular, so we can just use the Pythagorean theorem:

$$12^2+(12+16)^2=x^2\\ x=\sqrt{928}=4\sqrt{58}$$

Since MN is twice that, the answer is $$\boxed{8\sqrt{58}}$$

Jul 1, 2021

### 3+0 Answers

#1
+447
-1
Best Answer

Let P be the intersection point of MN and KL, and let x equal MP. You could use the intersecting chord theorem for this problem, but notice that the lines are perpendicular, so we can just use the Pythagorean theorem:

$$12^2+(12+16)^2=x^2\\ x=\sqrt{928}=4\sqrt{58}$$

Since MN is twice that, the answer is $$\boxed{8\sqrt{58}}$$

textot Jul 1, 2021
#2
+1540
+6

Important:

When two chords intersect inside a circle, then the measures of the segments of each chord multiplied with each other are equal to the product from the other chord.

~~~~~~~~~~~~~~~~~~~~~~~~~~~

LJ = 16

HJ = 40

LJ * HJ = MJ * NJ

640 = MJ * NJ

MN = √2560     or      16√10

If that answer's the best, then what's mine???

Jul 1, 2021
#3
+447
+1

lol sorry i got it wrong, just noticed it

OP plz change the best answer

My answer was supposed to be:

$$12^2+x^2=(12+16)^2\\x^2=640\\x=\sqrt{640}=8\sqrt{10}$$

and then multiply by 2

textot  Jul 7, 2021
edited by textot  Jul 7, 2021