CAT 1996 — QA Question 15

In a right-angled triangle, the length median to the hypotenuse is half the length of the hypotenuse. Hence, BD = $\frac{1}{2}$ AC = 3 cm. This relationship can be verified by knowing that the diameter of a circle subtends a right
angle at the circumference e.g. in the above figure D is the centre of the circle with AC as diameter. Hence,
∠ABC should be 90°. So BD should be the median to the hypotenuse. Thus, we can see that BD = AD = CD = Radius of this circle.
Hence, BD = $\frac{1}{2}$ diameter = $\frac{1}{2}$ AC = $\frac{1}{2}$ × hypotenuse.