Geometry is fun!
Geometry
Level
3
Common tangents of the three circles meet at A.Radius of the biggest circle is 18. B, C is point of contact of the tangent with the smallest circle.∠A =60 degree. Find area of ΔABC.Give your answer to three decimal place.
The answer is 5.196.
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1 solution
Let the points of contact of the upper tangent with the middle and the big circle be E & F respectively. Also let the radii of the middle circle and the small circle be x & y. Then we can write the following equations: 2√(18x))+2√(yx)+y √(3)=18√(3) ------(1), x²=18 y --------(2) which yield: x=6 & y=2. Then AB=AC=2√3 and area Tr. ABC=(1/2)(2√3)²sin(60°) = 3√3 = 5.196 s,u.