2020 · Q64
ABC is an equilateral triangle. The side BC is trisected at D such that BC = 3BD. What is the ratio of AD² to AB²?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A7:9
- B1:3
- C5:7
- D1:2
Explanation
With side s, AD^2 = s^2+(s/3)^2-2*s*(s/3)*cos60 = 7s^2/9 by the cosine rule. Thus AD^2/AB^2 = 7/9 - option (A). Numerically with s = 3: AD^2 = 9+1-3 = 7 = 7*9/9, confirming the ratio 7/9.