# Noah Atkinson

Geometry teacher | Tutor for 8 years

I am a dedicated educator specializing in Geometry, with a background in Mathematics from Washington and Lee University. My passion lies in guiding students through the intricate world of shapes, angles, and proofs, fostering their understanding and appreciation for the subject. With a commitment to clarity and patience, I strive to make geometric concepts accessible and engaging for learners of all levels. Through personalized instruction and effective problem-solving strategies, I aim to empower students to excel in their mathematical journey. Let's unlock the mysteries of Geometry together!

## Questions

Circle A has a center at #(2 ,-7 )# and a radius of #2 #. Circle B has a center at #(-3 ,6 )# and a radius of #1 #. Do the circles overlap? If not, what is the smallest distance between them?

Which is always a rhombus? Parallelogram, Trapezoid, Rectangle, or Square?

What is the perpendicular bisector of a line with points at A #(-33, 7.5)# and B #(4,17)#?

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?

What is the orthocenter of a triangle with corners at #(4 ,3 )#, #(7 ,4 )#, and (2 ,8 )#?

Point A is at #(3 ,2 )# and point B is at #(3 ,-8 )#. 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?

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 #10 #, #8 #, and #16 #, respectively. What is the rectangle's area?

Each exterior angle of a certain regular polygon measures 30. How many sides does the polygon have?

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?

Cups A and B are cone shaped and have heights of #38 cm# and #24 cm# and openings with radii of #12 cm# and #18 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

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?

A parallelogram has sides with lengths of #15 # and #8 #. If the parallelogram's area is #60 #, what is the length of its longest diagonal?

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 circle has a center that falls on the line #y = 5/9x +4 # and passes through # ( 3 ,1 )# and #(5 ,7 )#. What is the equation of the circle?

Two corners of a triangle have angles of #pi / 4 # and # pi / 3 #. If one side of the triangle has a length of #6 #, what is the longest possible perimeter of the triangle?

A parallelogram has sides A, B, C, and D. Sides A and B have a length of #3 # and sides C and D have a length of # 9 #. If the angle between sides A and C is #(7 pi)/18 #, what is the area of the parallelogram?

A line segment has endpoints at #(1 ,4 )# and #(4 , 9)#. The line segment is dilated by a factor of #1/3 # around #(4 , 2)#. What are the new endpoints and length of the line segment?

How do you find the volume of a 52 cm diameter spherical balloon?

A line segment goes from #(2 ,5 )# to #(3 ,2 )#. The line segment is dilated about #(5 ,4 )# by a factor of #3#. Then the line segment is reflected across the lines #x = 4# and #y=-2#, in that order. How far are the new endpoints form the origin?

Is it possible for two vertical angles to be complementary angles?