$A$ man of height $170 \, cm$ wants to see his complete image in a plane mirror (while standing). His eyes are at a height of $160 \, cm$ from the ground. Which of the following statements are correct?
$(a)$ Minimum length of mirror is $80 \, cm$
$(b)$ Minimum length of mirror is $85 \, cm$
$(c)$ Bottom of the mirror should be at a height $80 \, cm$
$(d)$ Bottom of the mirror should be at a height $85 \, cm$

• A
  $a, c$
• B
  $a, d$
• C
  $b, c$
• D
  $b, d$