HCU MCA 2013 Paper

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Question : 34 of 75

Marks: +1, -0

In an equilateral triangle, let h be the height and r be the radius of the circumcircle. Then, the ratio r : h, is

2 : 3
$2\π:√3$
$√3 :1$
$\π:√5/2$

Solution:

(a) Given that,

\;\;\;\;\;\;\;

CD = h

\;\;\;\;\;\;\;

OA = OB = OC = r
∴

\;\;\;\;

OD = h - r
Now, in △ OAD,
sin 30° =

\OD/\OA={\h-\r}/\r

⇒

\;\;\;

1/2={\h-\r}/\r

⇒

\;\;\;\;\;

r = 2h - 2r
⇒

\;\;\;

3r = 2h
∴

\;

r : h = 2 : 3

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