a chord of a circle is equal to the radius of the circle. find the angle subtended by the chord at a point on the minor arc and also at a poinnt on the major arc.
In the figure, BC is the chord which is equal to the radius.
Chord BC subtends angle BOC at the centre O , It subtends angle CAB at a pt on the major arc, and it subtends angle CDB at a pt on the minor arc.
In triangle COB
BC = OB = OC (radius)
Hence triangle COB is equialteral. In an equilateral triangle, all the angles are equal and are 60 degrees.
hence, angle COB = 60
angle CAB = 1/2 ( angle COB) ( CAB is the inscribed angle of minor arc BC)
= 60/2 = 30
angle CDB = 1/2/( reflex COB) ( CDB is the inscribed angle of major arc CB )
= 1/2( 360 - 60)
= 1/2 (300)
Hence the angle subtended on the major arc is 30 and the angle subtended on the minor arc is 150