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CAT 2008 — QA Question 10

Geometric CentersEasy
Passage / Data

Directions for next 2 questions:

The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.

In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

Answer & solution

  • A

    17.05

  • B

    27.85

  • C

    22.45

  • D

    32.25

  • 26.25

Solution

We know that the area (A) of triangle (ABC) is related to the circum radius (R) and sides of the triangle as follows:

R = AB×BC×AC4A

Where, Area (A) = ½ × AD × BC

∴ R = AB×BC×AC4×12×AD×BC = AB×AC2AD = 17.5×92×3 = 26.25 cm

Hence, option (e).

CAT 2008 QA Q10: In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on — Solution | TheCATExam