# Caroline Aucoin

Geometry teacher | Verified Expert

I hold a degree in Geometry from Montclair State University. With a passion for unlocking the mysteries of shapes and spaces, I guide students through the intricacies of geometric concepts. My teaching style emphasizes clarity and practical application, empowering learners to excel in problem-solving and critical thinking. Drawing on my academic background and real-world experience, I foster a supportive learning environment where curiosity thrives. Together, we'll explore the fascinating world of geometry and uncover its relevance in everyday life. Let's embark on this journey of discovery together.

## Questions

Circle A has a radius of #4 # and a center of #(6 ,1 )#. Circle B has a radius of #1 # and a center of #(5 ,3 )#. If circle B is translated by #<-2 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #8 # and the triangle has an area of #32 #. What are the lengths of sides A and B?

The North Campground (3,5) is midway between the North Point Overlook (1,y) and the Waterfall (x,1). How do I use the Midpoint Formula to find the values of x and y and justify each step? Please show steps.

Sherry spots a car as she is looking down at a 70° angle from the top of the Eiffel Tower, which is 1063 ft tall. How far away from the base of the tower is the car?

Is the answer choice I selected right?!

How would I find the area of a 45-45-90 triangle with one side of length 73?

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #21 # and the height of the cylinder is #2 #. If the volume of the solid is #90 pi#, what is the area of the base of the cylinder?

A line segment has endpoints at #(2 , 3)# and #(5 , 2)#. If the line segment is rotated about the origin by #(pi)/2 #, translated vertically by #3#, and reflected about the y-axis, what will the line segment's new endpoints be?

How many sides do these regular Polygons have if their interior is 30?

A composite geometry is made up of cube and a square pyramid frustum. The slanted side AK stretch a side lengths of 5.62 forming an isosceles triangle. Calculate the volume, surface area and sketch the net of the surface area?

A line passes through #(5 ,8 )# and #(2 ,9 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #42 # and the height of the cylinder is #1 #. If the volume of the solid is #225 pi#, what is the area of the base of the cylinder?

An ellipsoid has radii with lengths of #8 #, #8 #, and #12 #. A portion the size of a hemisphere with a radius of #6 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Circle A has a center at #(1 ,5 )# and an area of #18 pi#. Circle B has a center at #(8 ,4 )# and an area of #66 pi#. Do the circles overlap?

Two corners of an isosceles triangle are at #(2 ,4 )# and #(8 ,5 )#. If the triangle's area is #4 #, what are the lengths of the triangle's sides?

There is a rectangle with width #4x# and height #(7/3)x#. What is the area of the rectangle when #x = 6#?

A circle's center is at #(7 ,5 )# and it passes through #(5 ,8 )#. What is the length of an arc covering #(7pi ) /4 # radians on the circle?

A triangle has vertices A, B, and C. Vertex A has an angle of #pi/8 #, vertex B has an angle of #( pi)/4 #, and the triangle's area is #8 #. What is the area of the triangle's incircle?

A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #3 #, its base has sides of length #6 #, and its base has a corner with an angle of # pi/3 #. What is the pyramid's surface area?

A line segment has endpoints at #(8 ,4 )# and #(3 ,7 )#. The line segment is dilated by a factor of #1/2 # around #(3 ,2 )#. What are the new endpoints and length of the line segment?