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 #2
avatar+934 
+1

I know this is a lot, but this website has some info on creating a thesis. Usually a thesis is a brief statement that describes your whole paragraph.

 

Hope it helps!

 

I'm assuming that this is some sort of argumentative essay where you need text evidence to support your claims.

 

Your thesis goes against common thinking about standardized tests and why they aren't applicable to us now. This can capture the reades attention but it is much to brief because you go right into your reasoning. According to the website link, your thesis needs to answer the "So what" question on it's so important.

 #7
avatar+23245 
+2

I got the same answer that guest got, 108, but not in so nearly elegant way.

 

I placed the diagram on a coordinate axis, with P(0,0), C(4,0), and B(-14,0).

Since PA = 13, it is on a circle with center P and radius 13:  x2 + y2  =  13

-- I called the x-value of this point 'a', so the y-value became  sqrt(169 - a2).

 

I used the theorem that the center of a circle is on the perpendicular bisectors of the chords.

Since one chord is BP, its midpoint has x-value -7 and its y-value is on the line x = -7.

Since another chord is PC, its midpoint has x-value 2 and its y-value is on the line x = 2.

Another chord is AP: using its endpoints, I found its midpoint and its slope.

From these values, I could find the equation of its perpendicular bisector (not a lot of fun, for it had a lot of a-terms and square roots).

Then, I found the intersection of this perpendicular biscector with the line x = -7 and the intersection of this perpendicular bisector with the line x = 2 (there were still a lot of a-terms and square roots).

With these two points (the centers of the circumcircles), I could find the distance from one center to point P and the distance from the other center to point P (By this time, I was on a firt-name basis with the a-terms and square roots).

Since these are equal, by solving this equation, I could find the value of a, which was -5.

This is the x-value of point A, allowing me to find the y-value of point A, 12, which is the height of triangle ABC.

With the height 8 and the base 18, the area is 108.

Apr 7, 2020

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