Two circles have the same radius of 1cm. B & C are the center of the two circles.they have Intersected at A & D point.what is the area of ABCD?

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The both circles have the same radius of 1cm. B & C are the center of the two circles.they have Intersected at A & D point.what is the area of ABCD?

1 Answer
Shwetank Mauria
May 28, 2017

Area of ABCD is 1.22841.2284 cm^2cm2

Explanation:

Observe that AB=AC=CD=BDAB=AC=CD=BD and hence DeltaABC and DeltaBCD# are two equilateral triangles.

Hence /_ACD=/_ABD=120^@

Now if we join AD it divides the desired area of ABCD in two equal segments
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and area of each segment, say ABD, is area of respective sector with angle 120^@ minus area of triangle DeltaACD.

Area of sector is pixx1^2xx120^@/360^@=pi/3

and area of DeltaACD=1/2xx(2xxsqrt3/2)xx1/2=sqrt3/4

(Note that AD=2xxsqrt3/2 forms base of triangle and height is half of BC i.e. 1/2)

Hence area of ABCD iss 2xx(pi/3-sqrt3/4)

= 2xx(1.0472-0.4330)=2xx0.6142=1.2284 cm^2

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