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Where is the orthocentre of a right-angled triangle located?

Competition practiceGeometry
  • AAt the midpoint of the hypotenuse
  • BOutside the triangle
  • CAt the vertex of the right angle
  • DAt the centroid of the triangle

Step-by-Step Solution

The orthocentre is where the three altitudes meet. In a right-angled triangle each leg is itself the altitude to the other leg, so two of the altitudes are the legs, and they meet at the right-angle vertex. The third altitude, drawn from that vertex to the hypotenuse, passes through the same point. The midpoint of the hypotenuse is the circumcentre, a different centre altogether.
Answer: C) At the vertex of the right angle

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