Let S be the circle in x y -plane which touches the x -axis at point A , the y -axis at point B and the unit circle x²+y²=1 at point C externally. If O denotes the origin, then the angle OCA equals

Step-by-step solution

Slope of O M=1 COA =45^ C ( 1 2 , 1 2 ) Now OM =O C+C M 2 ~h =1+ h Squaring array l 2 h²=h²+1+2 h h²-2 h-1=0 array h = 2 8 2 h =1 2 ~A (1+ 2 , 0) Slope of A C= 0- 1 2 1+ 2 - 1 2 =- 1 2 +1 =-( 2 -1)=- 22 1 2 ^ = (180-22 1 2 )^ = 157 1 2 ^ CAX =157 1 2 ^ OCA =157 1 2 ^ -45^ =112 1 2 ^ = 5 8