In ΔABC, m∠B = 90 and AC = 10. The length of the median BM =

In Δ ABC, using the theorem of Apolloneous, we know that,

For BM to be the median, we have,

AB² + AC² = 2(BM² + CM²)

Also, as Δ ABC is right angled at B,

⇒ AB² + AC² = AC² = 10² = 100

⇒ 100 = 2 (BM² + 5²)

⇒ 50 = BM² + 25

⇒ BM = 5

∴ Option (a) is correct.