Understanding the Largest Empty Circle in a Diagram

The video tutorial explains how to place the largest empty circle on a diagram by analyzing distances between points E, F, and D. The process involves determining the circle's center, which is ideally at a vertex due to equal distance from surrounding points. The tutorial concludes by calculating distances to find the largest possible circle, with the center at either point V or W and a radius of the square root of 65.

What is the initial problem the teacher is trying to solve?

• Calculating the area of a triangle

• Determining the shortest path between points

• Placing the largest empty circle in a diagram

• Finding the smallest circle in a diagram

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

Why does the teacher want to move the center of the circle further apart?

• To ensure the circle is closer to point E

• To maximize the distance from points E, F, and D

• To avoid overlapping with other shapes

• To make the circle smaller

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

At what point is the circle equally close to points E and F?

• When the center is at point F

• When the center is at the midpoint between E and F

• When the center is at point D

• When the center is at point E

Tags

CCSS.HSG.CO.C.9

Why does the largest circle occur at one of the vertices?

• Because the vertices are the smallest points

• Because the vertices balance the distances from E, F, and D

• Because the vertices are the farthest from all points

• Because the vertices are the closest to point E

Tags

CCSS.HSG.CO.C.9

What happens when the center of the circle gets too close to point D?

• The circle becomes smaller

• The circle becomes larger

• The circle overlaps with point E

• The circle overlaps with point F

Tags

CCSS.3.MD.D.8

What is the significance of the vertices in determining the largest circle?

• They are the points where the circle can be the largest without getting too close to E, F, or D

• They are the points where the circle is the smallest

• They are the closest points to E

• They are the smallest points in the diagram

Tags

CCSS.3.MD.D.8

How does the teacher determine which vertex will have the largest circle?

• By measuring the distances from E to each vertex

• By measuring the distances from D to each vertex

• By measuring the distances from F to each vertex

• By guessing

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

Which vertices are identified as having equal distances and thus potential centers for the largest circle?

• E and F

• W and X

• V and X

• V and W

Tags

CCSS.7.G.B.4

What is the radius of the largest empty circle?

• Square root of 45

• Square root of 75

• Square root of 55

• Square root of 65

Tags

CCSS.HSG.GPE.B.7

Why does the teacher not take the time to do the distance formula in the video?

• Because the students already know it

• Because it is not necessary for the explanation

• Because the distances are already known

• Because it is too complicated

Tags

CCSS.HSG.GPE.B.7