Multiple choice

In $\triangle ABC,\quad AD\, \, \, $ is median and E is the mid-point of AD. If BE is extended. it meets AC in F. AB=8 cm. BC = 21 cm and AC = 15 cm. then AF=

  1. 7 cm

  2. 3 cm

  3. 12 cm

  4. 5 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In triangle ABC, AD is a median. E is midpoint of AD. BE extended meets AC at F. By Van Schooten's or Menelaus theorem, or using mass point geometry: assign mass 1 to A and 1 to C (since AD is median, D is midpoint of BC, mass at D is 2). E is midpoint of AD, so mass at E is 2. Since BEF is a line, mass at F must balance. AF/FC = 1/2. Since AC = 15, AF = 15 * (1/3) = 5 cm.

AI explanation

Apply the basic proportionality theorem to triangle ADC, where E is the midpoint of AD, making DE equal to AE. Since EF is parallel to DB, it cuts AC and AD proportionally, meaning F is the midpoint of AC. Therefore, AF is half of the given AC length of 15 cm, which equals 5 cm.

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