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CAT 1996 — QA Question 15

Geometric CentersEasy
Passage / Data

Direction: Answer the questions based on the following information.

A watch dealer incurs an expense of Rs. 150 for producing every watch. He also incurs an additional expenditure of Rs. 30,000, which is independent of the number of watches produced. If he is able to sell a watch during the season, he sells it for Rs. 250. If he fails to do so, he has to sell each watch for Rs. 100.

In ΔABC, ∠B is a right angle, AC = 6 cm, and D is the mid-point of AC. The length of BD is

Answer & solution

  • A

    4 cm

  • B

    6

  • 3 cm

  • D

    3.5 cm

Solution

In a right-angled triangle, the length median to the hypotenuse is half the length of the hypotenuse. Hence, BD = 12 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 = 12 diameter = 12 AC = 12 × hypotenuse.

CAT 1996 QA Q15: In ΔABC, ∠B is a right angle, AC = 6 cm, and D is the mid-point of AC. The length of BD is — Solution | TheCATExam