Answered

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What point of concurrency in a right triangle is also the midpoint of the hypotenuse?

A. orthocenter
B. centroid
C. circumcenter
D. incenter

Sagot :

sqdancefan

Answer:

  C. circumcenter

Step-by-step explanation:

You want to know which point of concurrency is the midpoint of the hypotenuse of a right triangle.

Orthocenter

The orthocenter is the point where altitudes meet. In a right triangle, this is the right angle vertex.

Centroid, Incenter

The centroid is the point where medians meet. It is always internal to a triangle.

The incenter is the center of the inscribed circle. It is the point where the angle bisectors meet. It is always internal to a triangle.

Circumcenter

The circumcenter is the point where the perpendicular bisectors of the sides meet. It is always the midpoint of the hypotenuse in a right triangle. The hypotenuse is a diameter of the circumcircle.

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Additional comment

The orthocenter and circumcenter will be external to an obtuse triangle.

In the attached figure, the various points of concurrency are labeled with their answer choice designators.

View image sqdancefan
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