Question

The orthocenter of an obtuse angled triangle lies_ _ _ _ _ .
$
  \left( a \right){\text{Outside the triangle}}{\text{.}} \\
  \left( b \right){\text{Inside the triangle}}{\text{.}} \\
  \left( c \right){\text{On the smallest side of the triangle}}{\text{.}} \\
  \left( d \right){\text{On the greatest side of the triangle}}{\text{.}} \\
$

Answer 1

Hint-In this question, we use the concept of orthocenter of triangle. The orthocenter of a triangle is the intersection of the three altitudes of a triangle. Remember, the altitude of a triangle is a perpendicular segment from the vertex of the triangle to the opposite side.

Complete step-by-step solution -
Suppose we have an obtuse triangle $\vartriangle ABC$ , where obtuse angle at B.
Now, we know the orthocenter of a triangle varies with the different types of triangles.
So, we create the altitude from each vertex of the triangle and observe where the all three altitudes meet.

          

Now, all three altitudes meet at a point H.
The point H is an orthocenter of triangle $\vartriangle ABC$.
We can see that the orthocenter is now outside the triangle because two out of the three altitudes cannot be drawn inside the triangle.
So, the correct option is (a).

Note-In such types of questions we have to find the locus of orthocenter by using the geometrical interpretation because locus of the orthocenter varies from different types of triangles. So, we would always keep in mind that in obtuse triangles orthocenter lie outside the triangle.