# 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

Triangle A has sides of lengths #12 ,24 #, and #16 #. Triangle B is similar to triangle A and has a side of length #8 #. What are the possible lengths of the other two sides of triangle B?

The length of a rectangle is 3 centimeters less than its width. What are the dimensions of the rectangle if its area is 108 square centimeters?

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 #3 #. If side AC has a length of #8 #, what is the length of side BC?

An ellipsoid has radii with lengths of #8 #, #7 #, and #7 #. 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?

How do you find the dimensions of a rectangle whose perimeter is 52 m and whose area is 160 m?

How to find the equation of the line which passes through the point of intersection of the lines 7x − 3y − 19 = 0 and 3x + 2y + 5 = 0, give that the line is parallel to the line with the equation y = 2x + 1?

Answer the following questions? 1) What the angle vertical to ∠NOM 2) What is the angle vertical to ∠TLK 3) Identify the pair of angles supplementary to ∠NOM 4) What the measurement of angles ∠1, ∠2, and ∠3 5) What is the measure of exterior ∠OPS?

What is the centroid of a triangle with corners at #(1 , 3 )#, #(6 , 9 )#, and #(2 , 7 )#?

What is the definition of an irregular quadrilateral?

If three sides are given as follows, in which case / cases is it possible to draw a triangle?

Two corners of an isosceles triangle are at #(7 ,9 )# and #(5 ,3 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

A triangle has corners at #(2 , 6 )#, #(3 ,9 )#, and #(4 ,8 )#. What is the radius of the triangle's inscribed circle?

What is the perimeter of a triangle with corners at #(6 ,5 )#, #(9 ,1 )#, and #(3 ,8 )#?

A line segment is bisected by a line with the equation # - 6 y + 2 x = 3 #. If one end of the line segment is at #( 4 , 8 )#, where is the other end?

A triangle has corners at #(2 ,5 )#, #(3 ,1 )#, and #(4 ,2 )#. What is the area of the triangle's circumscribed circle?

What is the orthocenter of a triangle with corners at #(5 ,4 )#, #(2 ,3 )#, and (3 ,8 )#?

Two rhombuses have sides with lengths of #7 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(3pi)/8 #, what is the difference between the areas of the rhombuses?

A circle has a chord that goes from #( 5 pi)/6 # to #(5 pi) / 4 # radians on the circle. If the area of the circle is #21 pi #, what is the length of the chord?

Circle A has a center at #(1 ,8 )# and an area of #32 pi#. Circle B has a center at #(2 ,3 )# and an area of #28 pi#. Do the circles overlap?

Two rhombuses have sides with lengths of #3 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(7pi)/8 #, what is the difference between the areas of the rhombuses?