Let the arc A C of a circle subtend a right angle at the centre O . If the point B on the arc A C , divides the arc A C such that length of arc A B length of arc B C = 1 5 , and O C = O A + O B , then + 2 ( 3 -1) is equal to

Step-by-step solution

aligned & c = a + b . .(1) & a c = a a + b a & 0= + 15^ .(2) & (1) b c = a b + b b & 75^ = 15^ + .(3) & (2) &(3) 75^ =- ^2 15^ + aligned = 75^ ^2 15^ = 1 15^ = 2 2 3 -1 (2) = - 15^ 15^ = -( 3 +1) ( 3 -1) c = -( 3 +1) ( 3 -1) a + ( 2 2 3 -1 ) b Now aligned & + 2 ( 3 -1) = -( 3 +1) ( 3 -1) + 2 ( 3 -1) 2 2 3 -1 & = -( 3 +1)^2 2 +4 & = -3-1-2 3 +8 2 & =2- 3 aligned