In a circle with centre O and radius 5 cm, AB is a chord of length 5[3] ([ ] indicates underoot) cm. Find tha area of sector AOB.....

Many ways of working it out.... on way is....

Drop a perpendicular from centre (i.e. O) on AB at D(say).

Now, since Triangle AOB is an isocelous triangle so... BD = 5[3]/2 cm

OA = r = 5 cm

Now, in right-anged triangle BOD sin LBOD = BD/OB = [3]/2 => LBOD = 60⁰

Now, area of sector AOB = pi x r² x L AOB / 360⁰ = pi x 25 / 6 ....