My name is Christina and I'm in 12th grade taking Math Anlyasis. The problem is

The points (3,4), (9.-2), and (-3,-2) define a circle and a triangle.

  1. find the areas of the circle and the triangle. Find the difference between their areas.

  2. Find the length of a side of a square with the same area as the triangle.

  3. Find the length of a side of a Square with the same are as the circle.

If you could get back to me as soon as possible, i would greatly apprciate it. If i could at lease get the formula(if there is one) on how to find the area of a circle that could at least get me started. Thank you

Hi Christina,

This first thing that you should do is draw a diagram.

I labeled the three points A, B and C. From the diagram notice that the distance between B and C is 12 units and the point A is 6 units above the line joining B and C. The midpoint (3,-2) of the line segment BC (I called it P), is thus 6 units from each of A, B and C. Hence the circle with center P and radius 6 passes through A, B and C.

The area of a circle of radius r is Pi x r2 and hence the area of this circle is Pi x 62 which is 36 x Pi square units.

The area of a triangle is  1/2 x base x height and thus the area of the triangle ABC is  1/2 x 12 x 6 which is 36 square units.

Can you complete the problem now?
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