ShmoopTube

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Here’s your shmoop du jour, brought to you by chords.

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Let’s make sweet, sweet music together.

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The diameter of this circle is 14.

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Lines JN and MK are perpendicular to each other.  What is the length of the chord JK? 

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And here are the potential answers...

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We’re not sure where this circle is headed, but given the bow tie, it must be someplace fancy.

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Okay, so this problem makes a big deal out of the fact that JN and MK are perpendicular…

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What do the lines’ perpendicularity tell us?

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It tells us that, because L is the midpoint of the circle…

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…angle JLK is, by rule, a right angle.

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The diameter of the circle is 14, which makes each radius 7…

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…so we now also know the length of both JL and KL.

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And whaddya know…by looking at our clock, it appears to be Pythagorean theorem time again…

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Our “a” and “b” are each 7…

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So when we take a squared plus b squared equals c squared…

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…we get 7 squared plus 7 squared equals c squared…

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49 plus 49 is 98…and the square root of 98 can simplify to 49 times 2…

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…or 7 square root of 2.

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Answer D.

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There’s actually another way we could have gone about things…

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We know that JKL is an isosceles triangle, given that it’s a right triangle and the

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length of both sides is equal.

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So we could have just used what we know about the ratio of sides in an isosceles triangle

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to tell us that the hypotenuse must be x square root of 2…

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…or, in this case, 7 square root of 2. Either way. It’s answer D.

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