Question

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

Answer 1

aloha!

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given: AC=AB=BC= 9 cm

to find: the radius.

construction: draw AD being the perpendicular bisector of side BC.

proof: we know that that ∠ADC would be equal to 90° by construction.

And BD = DC

Now,

∠B = 60° { given }
∠OBD = 30° { half of 60° as BO bisects ∠B }

in triangle OBD
cos 30° = $\frac{base}{hypotenuse}$
√3 / 2 =  $\frac{4.5}{hypotenuse}$
H = 3√3 cm.


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Answer 2

may this answer will help you