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ravi saini

· started a discussion

· 1 Months ago

bc (Question: 113081.0 )

where you have mentioned that ac is diameter

Question:
A rectangle ABCD is inscribed in a circle with centre O. If AC is the diagonal and \(\angle \)BAC = 30°, then the radius of the circle in term of BC  will be equal to:
Options:
A) \(\cfrac{\sqrt 3}{2}\)BC
B) BC
C) \(\sqrt{3}\) BC
D) 2 BC
Solution:
Ans: (b) 


Join B and O

Then \(\angle \)BOC = 2 \(\angle \)BAC = 60°

Draw OM \(\perp \) from O on BC then BM = \(\cfrac{1}{2}\) BC

\(\therefore\) \(\angle \)BOM = 30°

From \(\triangle\)BMO

\(\cfrac{BM}{BO}=\ sin\ 30^o=\cfrac{1}{2}\)

\(\therefore\) OB = 2 BM

\(=2\times \cfrac{1}{2}BC\ = BC\)

So radius of circle will be equal to BC.

Knowledge Expert

· commented

· 1 Months ago

Hi,

rectangle ABCD inscribed in circle means rectangle is made of two right triangles then a rectangle inscribed in a circle must have its diagonal as the diameter of the circle.

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