If the circumradius of an equilateral triangle be 10 cm,

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If the circumradius of an equilateral triangle be 10 cm, then the measure of its in-radius is

Firstly , we draw a figure of an equilateral triangle whose circumradius is 10 cm ,

Let AB = y cm.

∴BD =	y
	2

AD = √	y² -	y²	=	√3	y cm.
		4		2

∴ OD =	1	×	√3	y =	y	cm.
	3		2		2√3

OB = √BD² + OD²

OB = √	y²	+	y²	= √	4y²	=	y	cm.
	4		12		12		√3

∴	y	= 10 ⇒ y = 10√3	cm.
	√3

Hence, OD =	y	=	10√3	= 5 cm.
	2√3		2√3