an equilateral triangle of side 9 cm is inscribed in a circle find the radius of circle (no centroid theorem)
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Let the triangle ABC is an equilateral triangle of side 9 cm and AD is 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=9cm 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
AD=3✓3cm
Hence Radius of circle is 3✓3 cm
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