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

Cups A and B are cone shaped and have heights of #16 cm# and #12 cm# and openings with radii of #6 cm# and #8 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?

Calculate the area for the trapeze #PQRS# ? (See question)

A cone has a height of #27 cm# and its base has a radius of #16 cm#. If the cone is horizontally cut into two segments #15 cm# from the base, what would the surface area of the bottom segment be?

A circle's center is at #(4 ,6 )# and it passes through #(3 ,1 )#. What is the length of an arc covering #(pi ) /3 # radians on the circle?

A figure is rotated #180^circ#. If one of the points on the image is G'(4, -8), what were the coordinates of G?

How do you find the radius of a circle if the circumference is #29pi#?

A circle has a center that falls on the line #y = 7/6x +1 # and passes through #(9 ,8 )# and #(2 ,5 )#. What is the equation of the circle?

A triangle has corners at #(7 ,1 )#, #(8 ,2 )#, and #(5 ,9 )#. How far is the triangle's centroid from the origin?

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #33 # and the height of the cylinder is #13 #. If the volume of the solid is #232 pi#, what is the area of the base of the cylinder?

How do you find the area of a parallelogram with base b = 87 cm and height h = 18.6 cm?

You are constructing a tangent line from a point outside a given circle to the circle. What two objects should you draw first?

Let #P(a,b) and Q(c,d)# be two points in the plane. Find the equation of the line #l# that is the perpendicular bisector of the line segment #bar(PQ)#?

A cone has a height of #16 cm# and its base has a radius of #2 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?

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #9 # and the height of the cylinder is #12 #. If the volume of the solid is #15 pi#, what is the area of the base of the cylinder?

If a pair of supplementary angles has the measures: 2x° and (x+30)°, what is the measurement of the larger angle?

A triangle has two corners of angles #pi /12# and #(7pi)/8 #. What are the complement and supplement of the third corner?

Circle A has a center at #(-2 ,-1 )# and a radius of #3 #. Circle B has a center at #(-8 ,3 )# and a radius of #1 #. Do the circles overlap? If not what is the smallest distance between them?

A parallelogram has sides with lengths of #9 # and #8 #. If the parallelogram's area is #32 #, what is the length of its longest diagonal?

What is the value of #sqrt(7)#?