# 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

Prove that the largest isosceles triangle that can be drawn in a circle, is an equilateral triangle?

What is the perimeter of a triangle with corners at #(3 ,7 )#, #(1 ,1 )#, and #(4 ,3 )#?

If the altitude of an equilateral triangle is #8sqrt3#, what is the perimeter of the triangle?

What is the measure of an angle whose measure is 50 more than the measure of its complement?

If angle A and B are complementary and #A=5x+8# and #B=x+4#, what are the measurements of each angle?

A parallelogram has sides with lengths of #16 # and #5 #. If the parallelogram's area is #48 #, what is the length of its longest diagonal?

What is the equation of the circle with a center at #(5 ,7 )# and a radius of #6 #?

A line segment has endpoints at #(2 , 3)# and #(1 , 2)#. If the line segment is rotated about the origin by #(pi)/2 #, translated vertically by #3#, and reflected about the x-axis, what will the line segment's new endpoints be?

Point A is at #(-8 ,5 )# and point B is at #(-3 ,-2 )#. Point A is rotated #pi/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

What is the formula for finding the area of an oval?

A cone has a height of #12 cm# and its base has a radius of #4 cm#. If the cone is horizontally cut into two segments #7 cm# from the base, what would the surface area of the bottom segment be?

Points A and B are at #(4 ,7 )# and #(3 ,9 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #4 #. If point A is now at point B, what are the coordinates of point C?

The perimeter of a square is 4 times as great as the length of any of its sides. Is the perimeter of a square is proportional to its side length?

A cone has a height of #12 cm# and its base has a radius of #7 cm#. If the cone is horizontally cut into two segments #3 cm# from the base, what would the surface area of the bottom segment be?

A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #12 #, #3 #, and #5 #, respectively. What is the rectangle's area?

Work out the size of one interior angle of a regular 15-sided polygon?

What is the equation of the tangent planes to #7x^2-3y^2-z^2+21=0# which passes through the line #7x-6y+9=0#,#z=3#?

Two corners of a triangle have angles of # (7 pi )/ 12 # and # pi / 8 #. If one side of the triangle has a length of # 2 #, what is the longest possible perimeter of the triangle?

How do you use Heron's formula to find the area of a triangle with sides of lengths #7 #, #4 #, and #7 #?

A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/4 #, and the triangle's area is #25 #. What is the area of the triangle's incircle?