Question

Let chord CD is parallel to tangent to circle at point A as shown in figure CD = 2, ∠CAD= Π/3, then area of ΔCAD is ? (A) √3 (B) 4√3 (C) 16√3 (D) 4

Answer 1

(A) `sqrt(3)`

Explanation:

Note that `abs(AC) = abs(AD)`
`color(white)("XXX")`(if this isn't clear as to why, ask)
Therefore
`color(white)("XXX")/_ACD=/_ADC`
and since `/_CAD = pi/3`

`color(white)("XXX")/_ACD=/_ADC=/_CAD (=pi/3)`

Therefore
`color(white)("XXX")abs(AC)=abs(AD)=abs(CD)=2`

Therefore the semi-perimeter is (2+2+2)/2 =3#

and by Heron's Formula for the area of a triangle
`color(white)("XXX")"Area"_triangle = sqrt(s(s-a)(s-b)(s-c))`

The area of the given triangle is
`color(white)("XXX")sqrt(3(3-2)(3-2)(3-2))=sqrt(3)`