2020 · Q85
AD is the median of the triangle ABC. If P is any point on AD, then which one of the following is correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AArea of triangle PAB is greater than the area of triangle PAC
- BArea of triangle PAB is equal to area of triangle PAC
- CArea of triangle PAB is one-fourth of the area of triangle PAC
- DArea of triangle PAB is half of the area of triangle PAC
Explanation
D bisects BC so triangles PBD and PCD have equal areas; subtracting from the equal areas ABD and ACD gives area(PAB) = area(PAC). Hence option (B). This holds for any point P on the median, not just for D itself.