Find area of square. ............ #maths #geometry #circle #olympiad #cds #cat #522 #cbse #ssc #cgl

Added: 2026-05-16

[00:00:00]This amazing question given to us is a circle and a square inside the circle passing through the center of the circle.

[00:00:08]This chord which is passing through the vertex of square, its length is given as 7 + 4 cm.

[00:00:15]Now exciting part is with this data we have to find the area of square.

[00:00:21]Solution is very short and simple.

[00:00:24]Let's start by extending this side length CD to meet the circle at point G.

[00:00:31]Now this angle D here, this is 90°.

[00:00:34]And with respect to circle we have got chord GC is there.

[00:00:38]And from center of circle a perpendicular is drawn.

[00:00:41]So by theorem, the perpendicular from center of circle on a chord bisects the chord.

[00:00:48]So if DC length is A, then GD length will be same A cm.

[00:00:54]Now again with respect to circle, we have chord FE is there and GC is there intersecting at point D.

[00:01:02]Applying intersecting chord theorem or power of point theorem, we get GD times of DC.

[00:01:09]That's equals to ED times of DF.

[00:01:12]Putting the values here, we get A times of A is 7 times of 4.

[00:01:19]Or A squared is 28 and that's the magic.

[00:01:23]A squared is nothing but area of square which you have to find. So area of this given square is 28 cm squared and that's our answer. I hope you enjoyed the solution. I will see you in next video.

[00:01:36]Till then, ta-ta, bye-bye.