Which figure has an orthocenter outside the triangle ? ?

The orthocenter is only outside of a triangle when the triangle is obtuse. The only obtuse triangle shown is the 25-45-110 triangle.

Solution:

Orthocenter: The point of intersection of Perpendicular bisectors of sides of Triangle is called Orthocenter.

→The Orthocenter of Acute angle Triangle lies inside the Triangle.

So, Triangle 1, and Triangle 2, lies inside the triangle.

→The Orthocenter of Right angled triangle lies on mid point of hypotenuse, So Triangle 4, has orthocenter on mid point of Hypotenuse.

→The Orthocenter of Obtuse Angle Triangle lies outside the Triangle, so orthocenter of triangle 3, lies outside the Triangle , in front of angle 110°.

Triangle 3, having angle measurement, 110°, 45°,25° is correct choice among four Triangles whose orthocenter lies outside the Triangle.

the answer is d

hope this