Question

20. An equilateral triangle of side 9 cm is inscribed in
a circle. Find the radius of the circle.
​

Answer 1

$\LARGE{ \underline{\underline{ \pink{ \bf{Required \: answer:}}}}}$

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

AD 2 + (9/2)2 = 92 = AD2 = 81 - 81/4 = 243/4

AD = 9/3/2

Radius = 2/3 AD = 2/3 x 9√3/2% = 3√3 cm

Answer 2

Answer:

$\bold{ \underline {\red{refer \: o \: the \: attachment \: for \:the \: explaination}}}$