# 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

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 #21 #, what is the length of side BC?

Verify that the Euler's formula is correct?

A chord with a length of #5 # runs from #pi/4 # to #pi/2 # radians on a circle. What is the area of the circle?

A cone has a height of #12 cm# and its base has a radius of #6 cm#. If the cone is horizontally cut into two segments #6 cm# from the base, what would the surface area of the bottom segment be?

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

The area of the trapezoid is 56 units². The top length is parallel to the bottom length. The top length is 10 units and bottom length is 6 units. How would I find the height?

How do you find the height of a parallelogram with an area of 104 square and a base of 8 yards?

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

Given right triangle ABC, with right angle at C, if b = 8 and c = 17, using the Pythagorean Theorem, what is a?

How do you write the standard equation of the circle the given center that passes with through the given point: center (5,9); point (2, 9)?

Can you construct a triangle that has side lengths 1 cm, 15 cm, and 15 cm?

What is an 11 and 12 sided shape called?

Given the surface #f(x,y,z)=y^2 + 3 x^2 + z^2 - 4=0# and the points #p_1=(2,1,1)# and #p_2=(3,0,1)# determine the tangent plane to #f(x,y,z)=0# containing the points #p_1# and #p_2#?

A triangle has corners at #(5 , 2 )#, #(2 ,3 )#, and #(3 ,4 )#. What is the radius of the triangle's inscribed circle?

Circle A has a center at #(4 ,-1 )# and a radius of #5 #. Circle B has a center at #(-3 ,2 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?

A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #2 # and #7 # 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?

What is the equation of the circle with a center at #(-4 ,6 )# and a radius of #3 #?

What is the perimeter of a triangle with corners at #(6 ,5 )#, #(9 ,2 )#, and #(3 ,8 )#?

A triangle has corners at points A, B, and C. Side AB has a length of #45 #. 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 #42 #, what is the length of side BC?

A parallelogram is determined by the vectors a = (-2,5) and b = (3,2). Determined the angles between the diagonals of the parallelogram?