CAT 2020 Quant Question [Slot 2] with Solution 20

Question

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 O. Then, the length of PQ, in meters, is nearest to

  1. 7.2
  2. 7.8
  3. 6.6
  4. 8.8
Option: 4
Solution:

\(AB = \sqrt {{3^2} + {4^2}}  = 5\)

\(OT = \frac{{3 \times 4}}{5} = \frac{{12}}{5}\)

\(OT = 2.4M\)

In \(\Delta OTQ\)

\(O{Q^2} = O{T^2} + T{Q^2} \Rightarrow T{Q^2} = O{Q^2} - O{T^2}\)

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

=19.24

\( \Rightarrow TQ = \sqrt {19.24}  \approx 4.4\)

\(\therefore PQ = 2TQ = 8.8m\)

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