Question

in triangle abc am is a median and n is the midpoint of am and bn produced meets AC at P prove that a b is equals to 1 upon 3 into AC hint take Q the midpoint of PC prove that MQ is parallel to BP extra.​

Answer 1

Given :-

• AM is the median of ΔABC .
• N is the midpoint of AM.

To Prove :-

• AP = (1/3)•AC

Construction :-

• Through M draw MG which is parallel to BP.

Solution :-

in ΔAMG we have ,

→ N is the midpoint of AM and NP is parallel to MG.

So,

P is midpoint of AG. { By converse of midpoint theorem .}

→ AP = PG -------------- Eqn.(1)

Similarly,

in ΔBCP we have,

→ M is the midpoint of BC and MG is parallel to BP.

So,

→ G is midpoint of CP.

→ PG = GC -------------- Eqn.(2)

From Both Equations , we get,

→ AP = PG = GC

Now,

→ AP + PG + GC = AC

→ AP + AP + AP = AC

→ 3AP = AC

→ AP = (1/3)•AC . (Proved.)

Answer 2

Step-by-step explanation:

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