CAT 2020 Exam Shift 3 Solved Paper

Question : 65 of 76

Marks: +1, -0

The vertices of a triangle are

(0,0),(4,0)

and

(3,9)

. The area of the circle passing through these three points is

Solution:

a=4, b=√{90} ; c=√{82}

Area of the triangle

=\;{1}/{2} × 4 × 9=18

The circumradius of the triangle

(R)=\;{a b c}/{4 ∆}

Area of the circle

=π R^{2}=π(\;{a b c}/{4 ∆})^{2}=\;{π(4 ⋅ √{90} ⋅ √{82})^{2}}/{(4 ⋅ 18)^{2}}

=π × \;{16 × 90 × 82}/{16 × 18 × 18}=\;{205}/{9} π

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