2019 · Q90
Consider the following statements:
- 1The perimeter of a triangle is greater than the sum of its three medians.
- 2In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD.
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
1: each median is shorter than the semi-sum of the two adjacent sides; adding the three gives sum of medians < perimeter. 2: AB+BD > AD and AC+CD > AD add to AB+AC+BC > 2AD. Both statements are correct.