hi Anurag
can you explain a little bit more how you came that AC and BD are the diameters of the circle
thanks

same doubt as clock60: its not given that BD is diameter??? AC = diameter (diagram suggests so)

Thanks Anurag, got it.

srcc25anu wrote:Quadrilateral ABCD is inscribed in circle K. The diameter of K is 20. AC is perpendicular to BD. What is the area of ABCD?

(1) AB = AD

(2) The length of CE is 8.

Quadrilateral ABCD is a kite..!! whose diagonals are intersecting at 90 degree, and area of kite is equal to product of its diagonals, we know one of the diagonals which is 20 as per the question, now lets just analyze the two statements.

1) AB=CD; we will not be able to find the length of the other diagonal of the kite by using this information hence 1 is not sufficient to answer the question.

2) CE=8, as we know that diameter ac of k is 20 therefore its radius is 10, i.e. CK=10, KE=CK-CE;

KE=10-8=2;

now draw draw the line connecting K to B, KB=10( radius of a circle);
as we know that in a circle, perpendicular drawn from the center of the circle bisects the chord, k is a center of the circle, and BD is chord, therefore BE=ED;

now in right angle triangle KEB; we have KB^2=BE^2+EK^2; KB=10,EK=2,BE=x;

100=x^2+4;
x=sqrt(96);

therefore BD= 2(BE)= 2sqrt(96);

therefore Area=1/2 AC*BD; 1/2 *20*2sqrt(96)= 20sqrt(96);

hence statement 2 alone is sufficient to answer the question hence B