Find the area of the quater as shown in the atachment

the answer is 5pi.

to understand how, assume a cartesian plane with O as origin, radius of circle as r. now assume coordinates of B as (rcosq, rsinq). and A is (r,0). now use distance formula between A and B and equate the distance to 4. this way we would have one equation in r and q. now write the equation of line BC, using the fact that it is perpendicular to AB. after writing the eqn, find coordinates of C by putting x coordinate zero. now apply distance formula between B and C. so we have another eqn in r and q. also, q lies in first quadrant. using these eqns, you will find that sinq= 4/5. and hence r^2=20. so, area of quarter circle is pi*r^2/4= 5pi