Q. 194.0( 15 Votes )
An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle.
Answer :
Let ABC be an equilateral triangle of side 9 cm.
And AD be one of its medians.
Then,
AD
BC
BD = (1/2) BC
⇒ BD = (1/2) 9 = 4.5 cm
In triangle ADB,
AD2 = AB2 - BD2
⇒ AD2 = 92 – (9/2)2
⇒ AD2 = 81 – (81/4)
⇒ AD = (9√3)/2
In an equilateral triangle the centroid and circumcenter coincide and AO: OD = 2: 1
∴ radius AO = (2/3) AD
= (2/3) (9√3)/2
= 3√3 cm
Hence, radius of circle = 3√3 cm.
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