Question

Pedal triangle of an obtuse angled triangle lies

• A. inside the triangle
• B. outside the triangle
• C. partially inside and partially outside the main triangle
• D. Doesn't exist

Answer 1

The correct option is C

partially inside and partially outside the main triangle

Pedal triangle is a triangle formed by joining the foot of the perpendiculars drawn from the vertices of the triangle to the corresponding sides of the triangle. In an obtuse angled triangle, two of the foot of perpendiculars lie outside the triangle and one inside. So, pedal triangle lies partially inside and partially outside as shown in the figure :

For $△ABC,O$ is the orthocentre and $△DEF$ is the pedal triangle. The shaded region of the pedal triangle lies outside the $△ABC$.