2015 · Q61
Consider the following statements :
- 1Let D be a point on the side BC of a triangle ABC. If area of triangle ABD = area of triangle ACD, then for all points O on AD, area of triangle ABO = area of triangle ACO
- 2If G is the point of concurrence of the medians of a triangle ABC, then area of triangle ABG = area of triangle BCG = area of triangle ACG.
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: [ABD] = [ACD] forces D to be the midpoint of BC; for O on median AD, [OBD] = [OCD], so [ABO] = [ABD]−[OBD] = [ACD]−[OCD] = [ACO] — true. Statement 2: the centroid's three triangles each have area one-third of ABC — true. Both correct (option C).