# Claire Akin

Geometry teacher | Verified Expert

I'm passionate about unlocking the mysteries of geometry for students. Armed with a degree from Saint Michael's College, I delve deep into shapes, angles, and proofs to make this abstract subject tangible and engaging. With years of experience, I've honed my ability to break down complex concepts into digestible chunks, ensuring every student grasps the beauty and logic of geometry. Let's navigate the world of lines and polygons together, turning confusion into clarity, one theorem at a time.

## Questions

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?

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?

Triangle A has sides of lengths #5 ,3 #, and #8 #. Triangle B is similar to triangle A and has a side of length #1 #. What are the possible lengths of the other two sides of triangle B?

What is the orthocenter of a triangle with corners at #(1, 3)#, #(6, 2)#, and #(5, 4)#?

Cups A and B are cone shaped and have heights of #39 cm# and #22 cm# and openings with radii of #17 cm# and #13 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?

How do we find the equation of perpendicular bisector of a segment whose end points are #(-2,-1)# and #(-18,-5)#?

An ellipsoid has radii with lengths of #3 #, #4 #, and #7 #. A portion the size of a hemisphere with a radius of #3 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

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

What is the orthocenter of a triangle with corners at #(3 ,1 )#, #(4 ,5 )#, and (2 ,2 )#?

A triangle has vertices A, B, and C. Vertex A has an angle of #pi/8 #, vertex B has an angle of #(5pi)/12 #, and the triangle's area is #28 #. What is the area of the triangle's incircle?

A triangle has corners at #(6 , 3 )#, #(3 ,5 )#, and #(2 ,9 )#. What is the radius of the triangle's inscribed circle?

An ellipsoid has radii with lengths of #6 #, #9 #, and #4 #. A portion the size of a hemisphere with a radius of #5 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

A line segment is bisected by a line with the equation # 7 y + x = 7 #. If one end of the line segment is at #(1 ,3 )#, where is the other end?

A triangle has corners A, B, and C located at #(2 ,3 )#, #(5 ,8 )#, and #(3 , 2 )#, respectively. What are the endpoints and length of the altitude going through corner C?

A triangle has corners at #(2 ,4 )#, #(8 ,6 )#, and #(7 ,9 )#. How far is the triangle's centroid from the origin?

If the volume of a sphere doubles, what is the ratio of the surface area of the new, larger sphere to the old?

Circle A has a center at #(2 ,7 )# and an area of #81 pi#. Circle B has a center at #(4 ,3 )# and an area of #36 pi#. Do the circles overlap? If not, what is the shortest distance between them?

A parallelogram has sides A, B, C, and D. Sides A and B have a length of #1 # and sides C and D have a length of # 6 #. If the angle between sides A and C is #(7 pi)/12 #, what is the area of the parallelogram?

Circle A has a radius of #2 # and a center of #(1 ,7 )#. Circle B has a radius of #2 # and a center of #(8 ,1 )#. If circle B is translated by #<-4 ,3 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Two opposite sides of a parallelogram each have a length of #16 #. If one corner of the parallelogram has an angle of #(11 pi)/12 # and the parallelogram's area is #72 #, how long are the other two sides?