Discussion

Explanation:

Since D is the midpoint of BC ⇒ AD is the median to BC

Using Apollonius theorem, we get

AB2 + AC2 = 2 × (AD2 + BD2)

∴ 32 + 42 = 2 × (AD2 + BD2)

∴ AD = 9+162-6.2512.5-6.256.25 = 2.5 cm

Alternately,

​​​​​​​The sides of the given triangle form a pythagorean triplet.

∴ The given triangle is a right triangle with BC as the hypotenuse.

Since D is the midpoint of the hypotenuse, D is the circum-center of the right triangle hence D is equidistance from all three vertices.

In a right triangle, circumradius = half of the hypoteneuse.

∴ DA = DB = DC = 5/2 = 2.5 cm.

Hence, option (c).

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