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Question
An equilateral triangle of side 9cm is inscribed in a circle. Find the radius of the circle.
Solution
Let ABC be an equilateral triangle of side 9cm and let AD one of its medians. Let G be the centroid of . ΔABC Then AG : GD = 2:1
WKT in an equilateral le Δ centroid coincides with the circum center
Therefore, G is the center of the circumference with circum radius GA
Also G is the center and . GD ⊥ BC Therefore,
In right triangle ADB, we have
`AB^2=AD^2+DB^2`
`⇒9^2=AB^2+DB^2`
⇒`AD=sqrt(81-81/4)=(9sqrt3)/2cm`
`∴Radius = AG=2/3AD=3sqrt3cm`
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