In ΔABC, ∠C = 90º. M and N are the mid-points of sides AB and AC respectively. CM and BN intersect each other at D and ∠BDC = 90º. If BC = 8 cm, then the length of BN is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 4√6 cm
Here, M and N are the midpoint of the sides AB and AC
MN || BC also MN = (1/2)BC
MN = 8/2 = 4 cm
Also, ΔNDM and ΔBDC are similar.
(ND/DB) = (NM/BC)
⇒ (ND/DB) = (4/8) = (x/2x)
So, NB = x + 2x = 3x
Also ΔCDB ∼ ΔNCB
So,
NB/CB = CB/DB
⇒ 3x/8 = 8/2x
⇒ 6x2 = 64
⇒ x2 = 64/6
⇒ x = (8/√6)
We have to find the value of BN
= 1x + 2x = 3x = 3 × (8/√6) = 24/√6 = 4√6 cm