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Consider the following statements: I. If three equal circles are drawn on the vertex of equilateral triangle in such a way that all the circles touch each other externally then the triangle is equilateral triangle. II. The circum centre of any triangle cannot be lie on its side.

Consider the following statements: I. If three equal circles are drawn on the vertex of equilateral triangle in such a way that all the circles touch each other externally then the triangle is equilateral triangle. II. The circum centre of any triangle cannot be lie on its side. Correct Answer Only 1

Given:

Two statements are given

Concept Used:

Basic concept of circle

Calculation:

As per given in the statement 1 the following figure can be drawn

Now, all three circles are equal so, Radius of all the circles is equal

∴ O’P = O’’R = O’’’Q      ---(1)

Also, O’’P = O’’’R = O’’Q      ---(2)

By adding equation (1) and (2) we get

∴ O’P + O’’P = O’’R + O’’’R = O’’’Q + O’’Q

⇒ O’O’’ = O’’O’’’ = O’O’’’

So, the triangle is equilateral triangle

∴ Statement 1 is correct

Now, In obtuse triangle the circum centre lies on the side of triangle

∴ Statement 2 is Incorrect

Hence, option (1) is correct

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