In the diagram, O is the centre of the circle,   PT is a tangent to the circle at A.  AÔB = 126°  and ABC = 27° .

1. Calculate PÂB.
2. Show that  OA is parallel to BC.

(b)        Each interior angle of a regular polygon is 20n° , where n is the number of sides.  Find the least value of n.

observation

The (a) part of the question which is based on circle and tangency principles was
not attractive to candidates as few of them attempted it.  Many candidates did not
see <OAB = <OBA = 27° .  Furthermore, since OA is a radius and PAC is a
tangent, <PAO = 90°.   Hence<PAB = 117° and ABC = 27° >>  OA//BC. Since
<AOB +<OBC = 180° and <OAB = <ABC = 27°.

The case was the opposite in the (b) part.  It was well attempted.  Most of them did well, scoring high marks.  Many were able to get the equation
20n² – 180n + 360 = 0 thus obtaining n = 3.