The diagram shows a circle with one equilateral triangle inside and one equilateral triangle outside. The ratio of areas of big triangle to the small triangle is n :1. Find the value of n.Correct answer is '4'. Can you explain this answer?

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The diagram shows a circle with one equilateral triangle inside and one equilateral triangle outside. The ratio of areas of big triangle to the small triangle is n :1. Find the value of n.

Correct answer is '4'. Can you explain this answer?

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The diagram shows a circle with one equilateral triangle inside and on...

Rotating the smaller triangle by 180°, we get the following figure.

From symmetry we can say R is the midpoint of BC.
So P and Q are also mid points of AB and AC
From the midpoint theorem:

Since two equilateral tringles are also similar triangle we know

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The diagram shows a circle with one equilateral triangle inside and one equilateral triangle outside. The ratio of areas of big triangle to the small triangle is n :1. Find the value of n.Correct answer is '4'. Can you explain this answer?

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