# Evelyn Arboleda

Geometry teacher | Verified Expert

I hold a degree in Geometry from Dakota State University. My passion lies in unraveling the intricacies of shapes and space, guiding students through the wonders of geometric concepts. With a knack for simplifying complex ideas, I foster a supportive learning environment where students thrive. Whether exploring angles, polygons, or proofs, I'm dedicated to illuminating the beauty and logic of Geometry. Let's embark on this geometric journey together!

## Questions

A line segment has endpoints at #(9 ,3 )# and #(5 ,4 )#. The line segment is dilated by a factor of #3 # around #(4 ,6 )#. What are the new endpoints and length of the line segment?

Circle A has a radius of #2 # and a center at #(7 ,1 )#. Circle B has a radius of #1 # and a center at #(3 ,2 )#. If circle B is translated by #<-2 ,6 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

How do you use Heron's formula to find the area of a triangle with sides of lengths #7 #, #3 #, and #9 #?

A circle's center is at #(3 ,4 )# and it passes through #(0 ,2 )#. What is the length of an arc covering #( pi ) /6 # radians on the circle?

What is the perimeter of a triangle with corners at #(1 ,2 )#, #(8 ,3 )#, and #(4 ,4 )#?

A triangle has corners at points A, B, and C. Side AB has a length of #9 #. The distance between the intersection of point A's angle bisector with side BC and point B is #6 #. If side AC has a length of #15 #, what is the length of side BC?

Cups A and B are cone shaped and have heights of #32 cm# and #37 cm# and openings with radii of #12 cm# and #19 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?

A triangle has corners at #(3, 4 )#, #( 6, 3 )#, and #( 7 , 2 )#. If the triangle is dilated by # 5 x# around #(1, 1)#, what will the new coordinates of its corners be?

A triangle has two corners with angles of # pi / 4 # and # (3 pi )/ 8 #. If one side of the triangle has a length of #3 #, what is the largest possible area of the triangle?

Given 3 circles with radius #r# positioned find the the radius #R# of the circumscribing circle in terms of the radius of the small circles #r#? If r = 5 cm what is the area of the circumscribing circle?

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 #18 #. What is the area of the triangle's incircle?

Circle A has a center at #(3 ,1 )# and an area of #15 pi#. Circle B has a center at #(5 ,2 )# and an area of #24 pi#. Do the circles overlap?

An ellipsoid has radii with lengths of #8 #, #6 #, and #5 #. A portion the size of a hemisphere with a radius of #6 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

A triangle has corners A, B, and C located at #(5 ,5 )#, #(3 ,9 )#, and #(4 , 1 )#, respectively. What are the endpoints and length of the altitude going through corner C?

A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #2 # and #1 # and the pyramid's height is #7 #. If one of the base's corners has an angle of #(5pi)/6#, what is the pyramid's surface area?

Two opposite sides of a parallelogram each have a length of #9 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #36 #, how long are the other two sides?

Two rhombuses have sides with lengths of #4 #. If one rhombus has a corner with an angle of #(11pi)/12 # and the other has a corner with an angle of #(3pi)/4 #, what is the difference between the areas of the rhombuses?

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 #13 #, #4 #, and #3 #, respectively. What is the rectangle's area?

The radii of two concentric circles are 16 cm and 10 cm. #AB# is a diameter of the bigger circle. #BD# is tangent to the smaller circle touching it at #D#. What is the length of #AD#?

Triangle A has an area of #5 # and two sides of lengths #9 # and #3 #. Triangle B is similar to triangle A and has a side with a length of #25 #. What are the maximum and minimum possible areas of triangle B?