Find the area of the square ABCD.|| A circle with center E, touches side AD. | RS = 1 unit. #Tangent

In this video clip, we will find the area of the square. A circle is drawn such that it touches one side of the square and RS = 1unit from the diagram given.

#Tangent_radius_theorem
#Pythagoras_theorem

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[matheuslopes]

Side of square= 2S

We have a Chords Theorem arrangement where RS x s equals CR x RB

The diameter splits the side of the square in two equal halves, therefore 2S/2, which equals S

So, 1 x 2S= S X S
2S= S²
Cancelling S from both sides, we have S=2
but S is just half of the square side. The full length is 2S, which means 2 x 2- which means 4

Therefore, the side of square ABCD is 4. And the area, being side squared, is 4², therefore 16.

Answer: Area is 16

[shrikrishnagokhale]

Can we find area of the circle?
I found it.

[Константин-лкэ]

your explanation is too long: by theorem KR × 1 = CR × RB, therefore (x/2)^2=x, done