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CBSE Class 10 Answered

an equilateral triangle of side 9 cm is inscribed in a circle find the radius of the circle

Asked by atyagi.salesforce | 14 Oct, 2019, 10:55: PM
Expert Answer
Let triangle ABC be an equilateral triangle of side 9 cm and AD is the median where G be the centroid of the triangle which divides median into 2:1.
GD is perpendicular to BC.
In right triangle ADB,
AD2 + DB2 = AB2 where AB = 9 cm and BD = 4.5 cm
 
AD2 + (9/2)2 = 92 
AD2 = 81 - 81/4 = 243/4
AD = 9√3/2
Radius = 2/3 AD = 2/3 × 9√3/2 = 3√3 cm
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