CAT 2020 Exam Shift 2 Solved Paper

Question : 70 of 76

Marks: +1, -0

Let

{C}

be a circle of radius 5 meters having center at

{O}

. Let

{PQ}

be a chord of

{C}

that passes through points

{A}

and

{B}

where

{A}

is located 4 meters north of

{O}

and

{B}

is located 3 meters east of 0 . Then, the length of

{PQ}

, in meters, is nearest to

Solution:

A B=√{3^{2}+4^{2}}=5

O T=\;{3 × 4}/{5}=\;{12}/{5}

O T=2.4 M

∆ O T Q

O Q^{2}=O T^{2}+T Q^{2} ⇒ T Q^{2}=O Q^{2}-O T^{2}

=(5)^{2}-(2.4)^{2}

=19.24

⇒ T Q=√{19.24} ≈ 4.4

∴ P Q=2 T Q=8.8 m

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