Question

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?

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?

Answer 1

Area of ABCD is `1.2284` `cm^2`

Explanation:

Observe that `AB=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

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`