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