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

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1 Answer
Dec 24, 2015

(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)