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

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

Question

03-07-2024
Mathematics

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 :

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sqdancefan sqdancefan · Answer 1 · 2024-07-03T21:14:34-04:00

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.

Sagot :

Orthocenter

Centroid, Incenter

Circumcenter

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