In a triangle ABC, AB = 12, BC = 18 and AC = 15. The medians AX and BY intersect sides BC and AC at X and Y respectively. If AX and BX intersect each other at O, then what is the value of √2 × OX?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. √23.
Length of median AX
⇒ 1/2 × √[2 × (AB2 + AC2) – BC2]
⇒ 1/2 × √[2 × (122 + 152) – 182]
⇒ 1/2 × √[2 × 369 – 324]
⇒ 1/2 × √414
⇒ 3/√2 × √23
We know that O is the centroid of the triangle and it divides the median in the ratio 2 : 1
Hence,
OX = 1/3 × AX = 1/3 × 3/√2 × √23 = √23/√2
Value of √2 × OX = √2 × √23/√2 = √23