Question

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

Answer 1

Answer:

radius of the circle​ = 3√3  cm

Step-by-step explanation:

Area of equilateral triangle = (√3/4) * s²

= (√3/4) * (9)²

= (√3/4) * 81

= (81√3)/4 cm²

Also,

Area of Same triangle :

= 3 * b/4√4a² - b²

= 3 * 9/4 * √4r² - 9²

= 3 * 9/4 * √4r² - 81

= 27/4 * √4r² - 81

Now,

81√3/4 = 27/4 * √4r² - 81

=> √4r² - 81 = 3√4

=> 4r² - 81 = 27

=> 4r² = 108

=> r² = 27

=> r = 3√3 cm

Therefore,

radius of the circle​ = 3√3  cm

Hope it helps!