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If the circumradius of an equilateral tr...

If the circumradius of an equilateral triangle ABC be 8 cm, then the height of the triangle is

A

12 सेमी.

B

16 सेमी.

C

6 सेमी.

D

8 सेमी.

Text Solution

Verified by Experts

The correct Answer is:
A
माना कि `Delta` की भुजा x cm है
`therefore` परिवृत्त की त्रिज्या ` = (x)/(sqrt(3))`
`implies 8 = x/(sqrt(3))`
`implies x = 8sqrt(3)`
`therefore BD = (BC)/4 = (8sqrt(3))/2 = 4sqrt(3)`
समकोण `DeltaABD `में,
`AD^2 = AB^2 - BD^2`
`implies AD^2 = (8sqrt(3))^2 - (4sqrt(3)) = 192 - 48`
`implies AD = sqrt(144) = 12 cm`
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