A circle touches two adjacent sides of a rectangle and at and respectively. The vertex of the rectangle lies on the circle. The length of the perpendicular from vertex to the chord is . Find the area of rectangle.
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One of the easy way to find the answer is taking the condition of the above figure which satisfies all the given conditions. Here the circle touches the rectangle at A and O , and side D lies on the circle.
Here, D O = 2 5
therefore A D = 2 5 2 , and C D = 2 2 5
hence required area = A D × C D = ( 2 5 ) 2 = 6 . 2 5 .
if anyone wants detailed solution than you are most welcome to ask me.