Sophia Alfred
Geometry teacher | Experienced educator in USA
I'm a Geometry expert, graduating from Shepherd University. My passion lies in unlocking the mysteries of shapes and spaces. With a knack for simplifying complex concepts, I empower students to conquer geometric challenges with confidence. Let's navigate the world of angles and proofs together!
Questions
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 #9 #. If side AC has a length of #24 #, what is the length of side BC?
How does the radius of a circle change if the circumference is doubled?
A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #6 #, its base has sides of length #1 #, and its base has a corner with an angle of # pi/3 #. What is the pyramid's surface area?
In a right triangle, if #a=3# and #b=6#, what is the value of #c#?
Point A is at #(2 ,9 )# and point B is at #(-8 ,-3 )#. 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?
Two corners of an isosceles triangle are at #(4 ,8 )# and #(5 ,7 )#. If the triangle's area is #3 #, what are the lengths of the triangle's sides?
A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #2 # and #12 # and the pyramid's height is #3 #. If one of the base's corners has an angle of #pi/4#, what is the pyramid's surface area?
Circle A has a center at #(1 ,8 )# and an area of #18 pi#. Circle B has a center at #(8 ,1 )# and an area of #45 pi#. Do the circles overlap?
Circle A has a radius of #1 # and a center at #(2 ,4 )#. Circle B has a radius of #3 # and a center at #(6 ,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?
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?
A triangle has corners A, B, and C located at #(7 ,3 )#, #(4 ,8 )#, and #(3 , 7 )#, 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 #9 # 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?
A chord with a length of #1 # runs from #pi/8 # to #pi/3 # radians on a circle. What is the area of the circle?
A triangle has two corners with angles of # pi / 4 # and # pi / 8 #. If one side of the triangle has a length of #8 #, what is the largest possible area of the triangle?
The coordinates of the vertices of triangle ABC are A(-1,3), B(1,2) and C(-3,-1). Determine the slope of each side of the triangle and use that information to determine if the triangle is a right triangle or not?
A circle has a radius of #6x^9y^5#. The area of a circle can be found using A = Pi(radius)^2. What is the area of this circle in square centimeters?
In a circle a diameter #AB# is drawn and on one side of it an arc #CD# is marked, which subtends an angle #50^@# at the center. #AC# and #BD# are joined and produced to meet at #E#. Find #/_CED#?
Circle A has a center at #(9 ,-2 )# and a radius of #4 #. Circle B has a center at #(-2 ,6 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?
What is the area of an equiangular triangle with perimeter 36?
A triangle has corners at #(1 , 2 )#, #(5 ,2 )#, and #(3 ,5 )#. What is the radius of the triangle's inscribed circle?