CAT 2021 Slot 1 QA Question 20: 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

Question

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

Accepted Answer

Place the regular hexagon with its centre at the origin and side length 2.
Take $A = (2, 0)$, $C = (-1, \sqrt{3})$ and $D = (-2, 0)$. Since $T$ is the midpoint of $CD$,
$T = ( -\dfrac{3}{2}, \dfrac{\sqrt{3}}{2} )$
Now apply the distance formula.
$AT^2 = (2 + \dfrac{3}{2})^2 + (0 - \dfrac{\sqrt{3}}{2

Suppose the length of each side of a regular hexagon ABCDEF is 2 cm. If TTT is the mid point of CDCDCD, then the length of ATATAT, in cm, is

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