CAT 2021 Slot 1 · Quant · Question 16

CAT 2021 Slot 1 previous year question on Polygons, with the answer and a step-by-step solution.

PolygonsGeometry and MensurationMultiple choiceMedium
Suppose the length of each side of a regular hexagon ABCDEF is 2 cm. If T is the mid point of CD, then the length of AT, in cm, is
  1. A
    \sqrt{15}
  2. B
    \sqrt{12}
  3. C
    \sqrt{14}
  4. D
    \sqrt{13}
Pick an option, then check.
Answer & solution

Answer: Option D

Place the centre of the hexagon at the origin, so the circumradius is 2 and A=\left( -2,0 \right), C=\left( 1,\sqrt{3}\right) and D=\left( 2,0 \right). Then T=\left( \frac{3}{2},\frac{\sqrt{3}}{2}\right), so AT=\sqrt{{\left( \frac{3}{2}+2 \right)}^{2}+{\left( \frac{\sqrt{3}}{2}\right)}^{2}}=\sqrt{\frac{49}{4}+\frac{3}{4}}=\sqrt{13} cm.

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