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Question

Find the length of side of an equilateral triangle inscribed in a circle of radius 4 cm. (3 = 1.73)

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Solution

Consider the figure below.


Let AB = BC = CA = a cm
We know that the median and the perpendicular bisector of an equilateral triangle coincide with each other.
DC = a2 cm

As it is given that ABC is an equilateral triangle, AD is the median. Therefore, O would be its centroid.Hence, O divides the median in the ratio 2:3.Now, OA= 23×AD 4 cm = 23×ADAD = 6 cm

In right triangle ADC, we have:

AC2 = AD2+DC2a2= 62+a22a2-a24= 364a2-a24= 363a24= 363a2 = 36×4a2 = 12×4a = 43a = 6.92
Thus, the side of the equilateral triangle is 6.92 cm.

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