A circle C is tangent to the x and y -axis in first quadrant at the points P and Q respectively. B C and A D are parallel tangents to the circle with slope -1 . If the points A and B are on the y -axis while C and D are on x -axis and area of figure A B C D is 900 2 sq . units. The radius of the circle is k then k 3 is equal to

Step-by-step solution

A B C D is a traperium and its area = 1 2 (a+b) h Where a+b 2 =E F (mid parallel) Arca =2 r ( EF ) Now equation of EF is y=-x+c ....(1) From equation (1) passes through ( r . r ) aligned & C =2 r & x + y =2 r , hence E=(2 r, 0) and F(0,2 r) & E F= 4 r^2+4 r^2 =2 2 r & Area A B C D=2 r 2 2 r=4 2 r^2 & 4 2 r^2=900 2 , r^2=225 r=15 aligned