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If side of an equilateral triangle is \( \Large 20 \sqrt{3} cm \), then numerical value of the radius of the circle circumscribing the triangle is

A) 20 cm
B) \( \Large 20 \sqrt{3} cm \)
C) \( \Large 20 \pi cm \)
D) \( \Large \frac{20}{ \pi } cm \)

Correct Answer:

A) 20 cm

Description for Correct answer:

Here as the triangle is an equilateral triangle, so here the altitude drawn from each vertex 0 triangle meet at a common point and it can be called centroid.

\( \Large AB=BC=AC=20\sqrt{3} cm \)

\( \Large \therefore BD=DC=EC=EA=AF=BF \)

= \( \Large \frac{20\sqrt{3}}{2} = 10\sqrt{3} \)

\( \Large Now\ in\ \triangle ADB \)

\( \Large \left(AD\right)^{2}= \left(AB\right)^{2}- \left(BD\right)^{2} \)

=\( \Large \left(20\sqrt{3}\right)^{2}- \left(10\sqrt{3}\right)^{2} \)

=\( \Large 1200 - 300 = 900 \)

\( \Large \therefore AD = 30 cm \)

Now AO : OD = 2 : 1

\( \Large \therefore 2x+1x=30 \)

\( \Large \therefore AO = r = 2x = 20 cm \)

Part of solved Triangle questions and answers : >> Elementary Mathematics >> Triangle

Comments

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