Question

A circle is circumscribed about a triangle with vertices A(3,-2), B(2,5), and C(-1,6). Find the coordinates of the circumcenter (the center of the circumscribed circle).

Answer #1

A circle is circumscribed about an equilateral triangle, and
another circle is inscribed in the triangle. What is the ratio of
the area of the larger circle to the area of the smaller
circle?

Let O be the center of circumscribed circle of ABC triangle. Let
a, b, c be the vectors pointing from O to the vertexes. Let M be
the endpoint of a + b + c measured from O. Prove that M is the
orthocenter of ABC triangle.

Find the coordinates of the center, the foci, and the vertices
of the ellipse with equation
25(?−3)2 +9(?+7)2 =225

Find the center of mass of the triangle with vertices (-2,-2),
(4,-2), and (4,4). SOLVE THIS PROBLEM USING CALCULUS. DO NOT USE
ALGEBRA TO SOLVE THIS. BE DETAILED AND BE NEAT.

(b) The two vertices that form the non-congruent side of an
isosceles triangle are (−5, 2) and (2, 2). What are possible
coordinates of the other vertex?

Consider the function f:R?R given by f(x,y)=(2-y,2-x).
(b) Draw the triangle with vertices A = (1, 2), B = (3, 1), C =
(3, 2), and the triangle with vertices f(A),f(B),f(C).
(c) Is f a rotation, a translation, or a glide reflection?
Explain your answer.

Find the volumes of the solids generated by revolving the
triangle with vertices left parenthesis 2 comma 2 right
parenthesis, left parenthesis 2 comma 8 right parenthesis, and
left parenthesis 4 comma 8 right parenthesis about a) the x-axis,
b) the y-axis, c) the line xequals8, and d) the line
yequals2.
Type an exact answer, using
piπ
as needed, or round to the nearest tenth.)

2.0 pC charges sit at the vertices of an equilateral triangle of
a side .24 m.
a) Sketch the situation and show the electric field vectors and
show the net electric field at the center of the triangle.
b) Find the electric field at the center of the triangle.
c) Repeat the calculation if one of the charges is replaced by a
-2.0 pC charge.
Thank you!

Find, correct to the nearest degree, the three angles of the
triangle with the given vertices.
P(2,
0), Q(0,
1), R(4, 3)
∠RPQ =
∠PQR =
∠QRP =

Triangle has vertices, A(6,9), B(4,6) and C(-2,10). Which of the
following is true?
One of these 4
ABC is isosceles
ABC is right-angled
ABC is obtuse
ABC is equilateral

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