To find whether an atom in an organic molecule is chiral or achiral use the following flow chart.

If two or more ligands on a tetrahedral atom in a molecule form a ring, to determine whether they are different or not, use the following procedure.

Consider 1

Two of the ligands on C-1 in 1 are a hydrogen atom and a methyl group.  The other two ligands form a ring.  To determine whether they are identical or not, convert them to two hypothetical ligands:

Step 1: Number the rest of the carbon atoms in the ring for identification purposes in any way you wish.

Step 2:  Break the bond connecting C-1 and C-6.

Step 3:  The bond broken in Step 2 connected C-6 to a carbon atom (C-1).  Therefore, connect C-6 to a C atom that bears no ligands.

Step 4:  Break the bond connecting C-1 and C-2 in 1.

Step 5:  The bond broken in Step 4 connected C-2 to a carbon atom (C-1).  Therefore, connect C-2 to a C atom that bears no ligands.

Hypothetically, the four ligands on C-1 in 1 are as follow.

Notice that the two ligands that form the ring are identical.  Thus, the four ligands on C-1 in 1 are not different.

i.  The chiral centers are marked with a red asterisk.

ii.  The chiral centers are marked with a red asterisk.