Understanding the Circumcenter of a Right Triangle

What is the main goal of the video regarding the circumcenter of a right triangle?

• To demonstrate it is the longest side

• To show it is the center of the circle

• To establish it is the shortest side

• To prove it is the midpoint of the hypotenuse

What is the significance of point M in the construction?

• It is the endpoint of the hypotenuse

• It is the midpoint of the hypotenuse

• It is the midpoint of leg BC

• It is the circumcenter

Which triangles are shown to be similar in the video?

• Triangles OBM and ABC

• Triangles OAC and ABC

• Triangles OBC and ABC

• Triangles OAB and ABC

What is the ratio of BM to BC in the similar triangles?

• 1/3

• 1/4

• 1/2

• 1

What conclusion is drawn about point O in relation to the hypotenuse?

• O is outside the triangle

• O is the longest side

• O is the midpoint of the hypotenuse

• O is the endpoint of the hypotenuse

What property of point O is used to establish it as the circumcenter?

• It is equidistant from all vertices

• It is the longest side

• It is the endpoint of the hypotenuse

• It is the shortest side

What does it mean for a point to be equidistant from all vertices of a triangle?

• It is the midpoint of one side

• It is the center of the circle passing through all vertices

• It is the longest side

• It is the endpoint of the hypotenuse

What is the circumradius in the context of this video?

• The length of the hypotenuse

• The distance from O to the midpoint of BC

• The length of leg BC

• The distance from O to any vertex

How is the circumcenter related to the hypotenuse in a right triangle?

• It is the midpoint of the hypotenuse

• It is the longest side

• It is the shortest side

• It is the endpoint of the hypotenuse

What is the final conclusion about the circumcenter of a right triangle?

• It is the shortest side

• It is the midpoint of the hypotenuse

• It is the endpoint of the hypotenuse

• It is the longest side