MathematicsIn triangle ABC, E is the mid-point of median AD such that BE produced meets AC at F. If AC = 10.5 cm, then the measure of AF is ____ cm.

In triangle ABC, E is the mid-point of median AD such that BE produced meets AC at F. If AC = 10.5 cm, then the measure of AF is ____ cm.


AD is a median of triangle ABC and E is the midpoint of AD. BE produced meets AC in F, Prove that AF 1/3 AC

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    Solution:

    In triangle ABC, E is the mid-point of median AD such that BE produced meets AC at F. If AC = 10.5 cm, then the measure of AF is 3.5 cm.
    Given a triangle ABC in which E is the mid-point of median AD such that BE produced meets AC at F and AC = 10.5 cm.
    AD is a median of triangle ABC and E is the midpoint of AD. BE produced meets AC in F, Prove that AF 1/3 ACUsing mid-point theorem,
    AF=FG   ------(1)
    Also, in triangle BCF,  FG=GC   ......(2)
    Now, from both equations
    AF=FG=GC   …… (3)
    ⇒AF+FG+GC=AC ⇒AF+AF+AF=AC   ⇒AF=AC ⇒AF= 1 3 AC   ⇒AF= 1 3 (10.5) ⇒AF=3.5cm  
    Hence, the measure of AF is 3.5 cm.
     
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