Suppose two tangents PA and PB are drawn to the circle centered at C (1,2) from the point P (16,7) . If the area of the quadrilateral PACB is 75 square units, then the radius of the circle is

Step-by-step solution

PC = (16-1)^2+(7-2)^2 = 250 Area of PACB = AP AC = xr =75 x = 75 r In triangle APC aligned & x ^2+ r ^2= PC ^2 ( 75 r )^2+ r ^2=250 & r ^4-250 r ^2+5625=0 & r ^4-225 r ^2-25 r ^2+5625=0 & ( r ^2-225 ) ( r ^2-25 )=0 & r ^2=225 x =15 & or r ^2-25=0 r =5 aligned