The angle between the tangents drawn from the origin to the circle (x-7)^2+(y+1)^2=25 is

Step-by-step solution

Equation of the circle: (x-7)^2+(y+1)^2=25 Center is at (7,-1) with radius r=5 . The tangents originate from the point P=(0,0) . Distance from P to center is d= (7-0)^2+(-1-0)^2 = 49+1 = 50 . The tangent at any point is perpendicular to the radius at that point, forming a right triangle with sides r=5 , d= 50 , and tangent length. Let be the angle between the two tangents. Then ( /2)=r/d . /2= (5/ 50 )= (1/ 2 )= /4 =2( /4)= /2 radians Converting to decimal: /2 1.5708 radians.