Question

$H$ is the orthocentre of $\Delta ABC$ and $X,Y,Z$ are the mid points of $AH,BH,CH$ then the point $H$ is:

• A. centroid of $\Delta XYZ$
• B. orthocentre of $\Delta XYZ$
• C. circumcentre of $\Delta XYZ$
• D. incentre of $\Delta XYZ$

Answer 1

The correct option is B orthocentre of $\Delta XYZ$

From the fig, $ABC$ is the triangle.

$H$ is the orthocentre of $△ABC$.

It is located at intersection of the altitudes of the triangle. i.e. $AD\perp BC,BE\perp AC,$ and $CF\perp AB$.

It is given that $X,Y$ and $Z$ are the midpoints of $AH,BH$ and $CH$.

$\therefore XY\parallel AB,XZ\parallel AC$ and $YZ\parallel BC$

$\therefore H$ is the orthocentre of $△XYZ$