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XAT 2019 — QA & DI Question 14

Basics of TrianglesMedium

The figure below shows two right angled triangles ∆OAB and ∆OQP with right angles at vertex A and P, respectively, having the common vertex O, The lengths of some of the sides are indicated in the figure. (Note that the figure is not drawn to scale.) AB and OP are parallel. What is ∠QOB?

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Answer & solution

  • A

    tan–1(2/3)

  • 45°

  • C

    60°

  • D

    30°

  • E

    tan–1(3/2)

Solution

Consider the figure given below.

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In ∆POQ, OQ = 12+22 = √5

In ∆AOB, OB = 12+32 = √10

In ∆DQB, QB = 22+12 = √5

Now, in ∆QOB, OB2 = OQ2 + QB2

⇒ ∆QOB is a right isosceles triangle, right angles at Q.

∴ ∠QOB = 45°

Hence, option (b).

XAT 2019 QA & DI Q14: The figure below shows two right angled triangles ∆OAB and ∆OQP with right angles at vertex A and P, respe — Solution | TheCATExam