Consider the following statements in respect of an equilateral triangle ABC.
1There is a point P inside the triangle ABC such that each of its sides subtends an angle of 120 degrees at P.
2There is a point P inside the triangle ABC such that the triangle PBC is obtuse angled and A is the orthocentre of triangle PBC.
Which of the above statements is/are correct?

Question

Consider the following statements in respect of an equilateral triangle ABC.

1There is a point P inside the triangle ABC such that each of its sides subtends an angle of 120 degrees at P.
2There is a point P inside the triangle ABC such that the triangle PBC is obtuse angled and A is the orthocentre of triangle PBC.

Which of the above statements is/are correct?

Accepted Answer

Option C: Both 1 and 2