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
Alan P.
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)#

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