Q9 of 31 Page 218

Three equal circles touch one another externally. Let us prove that the centres of the three circles form an equilateral triangle.


Let three equal circles be there with centre A, B and C


Let the radius of each circle be equal to r since all the circles are equal


Since the three circles touch each other externally so the length of each side of the triangle is a sum of the radius of each circle.


So we can say each side of the triangle is equal to


AB = 2r


BC = 2r


CA = 2r


Since AB = BC = CA, so we can say that the triangle is equilateral.


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