Three circles each of radius root 3cm ,are drawn touching each other externally. Another circle is drawn enclosing and touching all three. What is the area of the big circle ?
there are three small circle with radius root 3 cm and centers A, B and C respectively.
ABC will be an equilateral triangle, and its circum-center will be the circum-centre for the bigger circle.
let O be the circum-center of the triangle ABC.
ABC is an equilateral triangle where AC=2 *root3
∠AOC=360/3=120
since OA=OC
∠OAC=∠OCA=(180-120)/2=30 deg
,
area of the big circle is