Question

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

Answer 1

Hey !!! ^_^

Here is your answer

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Let ABC be an equilateral triangle of side 9cm
and let AG be radius of the Circle

and Let G be the centroid of ▲ABC ..

So ,

AG : GD = 2:1
( Following coordinate geometry formula)


G is the center of Circumference with circum radius GA

Also , G is the center and GD perpendicular on BC ...

Now in ▲ ABC ..

AB² = AD² + DB²

$ad \: = \sqrt{81 - \frac{81}{4} } \\ \\ ad = \frac{9 \sqrt{3} }{2} cm \\ \\ ag = \frac{2}{3} ad \\ \\ ag = \frac{2}{3} \times \frac{9 \sqrt{3} }{2 } \\ \\ ag = 3 \sqrt{3} cm$
Therefore radius of circle is 3√3cm

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I HOPE IT WILL HELP YOU

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