Answer :


Given: Equilateral triangle of side 9 cm is inscribed in a circle.


Construction: Join OA, OB, OC and drop a perpendicular bisector from center O to BC.


Here,


Area (ΔABC) = 3× area (ΔOBC)


Area (ΔABC) = a2 = × 92 =


Now,


Area (ΔOBC) = × AC × OD = × 9 × OD


We know that,


Area (ΔABC) = 3× area (ΔOBC)


= × 9 × OD


OD =


Now, in ΔODC


By Pythagoras theorem


OC2 = OD2 + DC2


OC2 = 2 + 2


OC2 = + = = 27


OC =


Radius = OC =

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