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What is MN?

 

 Jul 1, 2021

Best Answer 

 #1
avatar+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
 #1
avatar+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
avatar+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??? laugh

 Jul 1, 2021
 #3
avatar+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

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