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Three points are P (-2, 7), Q (2,3), and R (4, 5). Find the equation of the circle which passes through points P, G, and R.

Thanks lots to anyone who helps. liz x

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- Thread starter liz
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- #1

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Three points are P (-2, 7), Q (2,3), and R (4, 5). Find the equation of the circle which passes through points P, G, and R.

Thanks lots to anyone who helps. liz x

- #2

Galileo

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Suppose you draw a circle and pick two arbitrary (different) points on that circle. What construction with only these points would allow you to draw a line that passes through the center of the circle?

Once you know this, you can apply it to 2 pairs of points from P,Q,R and construct the center.

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TD

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- #4

HallsofIvy

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(x- a)

Since the circle passes through (-2, 7), x=-2, y= 7 must satisfy that:

(-2-a)

Do the same with the other two points and you have 3 equations to solve for the 3 unknowns a, b, and R.

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liz said:Three points are P (-2, 7), Q (2,3), and R (4, 5). Find the equation of the circle which passes through points P, G, and R.

It always helps plot given points because the question might present a special case.

It also helps a lot use graph paper.

After you plot these points you might notice that PQ and QR go through the grid intersictions in a special way.

Can you prove what you see? There is a certain rule you should apply.

Since a triangle PQR is special, there is an interesting property of the center of its circumcircle. It makes it a snap to find its coordinates and radius, and equation of the circle.

If you get stumped I'll be happy to help you along.

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