# SAT Math: Calculating a Circle's Radius When Given Its Center and a Point on Its Circumference

What is the radius of a circle with a center at (-4, 5) and a point on the circumference at (2, 13)?

 Product Type SAT Math SAT SAT Math SAT Math Additional Topics in MathGeometry and Measurement Test Prep SAT Math

### Transcript

00:18

from hurting it because math problems don't wear protective headgear

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Well here's a standard form circle where H K's a

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center Yeah you know this one Well plug in the

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centre point for H and K being careful about the

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signs Yeah I saw the sign song about that So

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we've got X plus four squared Plus Wyman five squared

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equals R squared were only given a random point on

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this circle And we can put that point to good

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use So just plug it in for X and y

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It's how easy this is We love circles so we

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get two plus four squared plus theta two minus five

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squared equals R squared Well six squared plus eight square

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It is you thirty six plus sixty fourths Hundreds are

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scared So are squared of one hundred which is in

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the radius of the circle Just ten Yeah well that

00:59

was one way to solve the problem Another way would

01:01

be with a distance formula the distance from the centre

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to any part of the circle's edge Is the radius

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rights basically the definition Well we could have used the

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distance formula to measure the distance from the center to

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a random spot on the edge by plugging in the

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values of the two points that were given like this

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So the distance is ah this thing And then we

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just plug in the negative four minus two squared plus

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five minus thirteen square there And that gets us formula

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Looks a whole lot like what we just did only

01:28

coming at it from a side view mirror Well either

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way works but whichever you choose tackle it gently so 00:01:33.23 --> [endTime] it's Mom doesn't get too worried and that's it