# 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

The sides of this polygon subtend angles of 36° at the centre of the polygon. How many sides does the polygon have?

A triangle has vertices #(6 ,3 )#, #(5 ,8 )#, and #(3 ,2 )#. What is the area of the triangle's circumscribed circle?

Two corners of a triangle have angles of #(3 pi ) / 8 # and # pi / 6 #. If one side of the triangle has a length of #3 #, what is the longest possible perimeter of the triangle?

A line segment has endpoints at #(2 ,8 )# and #(2 , 1)#. The line segment is dilated by a factor of #3 # around #(6 , 4)#. What are the new endpoints and length of the line segment?

Using the graph of f(x)= 1/x as a starting point, describe the transformations to get to #g(x) = 1/x-4#?

What is the orthocenter of a triangle with corners at #(2 ,8 )#, #(3 ,4 )#, and (6 ,3 )#?

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

In a 30-60-90 triangle, what is the length of the other leg and hypotenuse if the short leg is 5 in?

Circle A has a center at #(8 ,5 )# and an area of #100 pi#. Circle B has a center at #(4 ,2 )# and an area of #36 pi#. Do the circles overlap? If not, what is the shortest distance between them?

Two circles centered at (2,3) and (4,7) intersect each other. If their radii are equal, then the equation of their common chord is ?

A triangle has corners at points A, B, and C. Side AB has a length of #8 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #9 #, what is the length of side BC?

A triangle has corners at points A, B, and C. Side AB has a length of #15 #. The distance between the intersection of point A's angle bisector with side BC and point B is #12 #. If side AC has a length of #36 #, what is the length of side BC?

Two rhombuses have sides with lengths of #1 #. If one rhombus has a corner with an angle of #(5pi)/12 # and the other has a corner with an angle of #(7pi)/12 #, what is the difference between the areas of the rhombuses?

A triangle has corners A, B, and C located at #(7 ,6 )#, #(4 ,3 )#, and #(5 ,8 )#, respectively. What are the endpoints and length of the altitude going through corner C?

Can you dissect an equilateral triangle into acute isosceles triangles? What is the minimum number of acute isosceles triangles that the original triangle could be dissected into?

Two corners of a triangle have angles of # (5 pi )/ 12 # and # ( pi ) / 3 #. If one side of the triangle has a length of # 15 #, what is the longest possible perimeter of the triangle?

What is the equation of the line passing through (-3,-2 ) and (1, -5)?

A triangle has corners at #(7 ,8 )#, #(2 ,4 )#, and #(6 ,3 )#. If the triangle is dilated by a factor of #2 # about point #(6 ,12 ), how far will its centroid move?

Nanako said she drew a square pyramid and that all of the faces are triangles. Is this possible?

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 #16 #, #2 #, and #4 #, respectively. What is the rectangle's area?