2017 · Q85
Consider the following statements :
- 1The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.
- 2The point of intersection of the perpendiculars drawn from the vertices to the opposite sides of a triangle may lie on two sides.
Which of the above statements is/are correct ?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Statement 1 (the circumcenter, intersection of perpendicular bisectors) lies outside an obtuse triangle — true. Statement 2 (the orthocenter) is the right-angle vertex for a right triangle, which lies on two sides — true. Hence option (C) Both 1 and 2.