Question

If two angles of a triangle are ${40}^{\circ },{40}^{\circ }$, then the orthocenter of the triangle will be

• A. Inside the triangle
• B. Outside the triangle
• C. On the triangle
• D. It will always be inside the triangle.

Answer 1

The correct option is B

Outside the triangle

Let the third angle be 'x'
${40}^{\circ }+{40}^{\circ }+x=80\Rightarrow x={180}^{\circ }-{80}^{\circ }\Rightarrow x={100}^{\circ }$
Here, the triangle is an obtuse angle triangle.

• For Acute angled triangle the orthocenter lies inside the triangle.

• For Right angled triangle the orthocenter lies on the vertex of the triangle.

• For Obtuse angled triangle the orthocenter lies outside the triangle.