Postal or Sorting Assistants Model Paper 3 With Solutions

Question : 3 of 100

Marks: +1, -0

The ratio of the areas of the inscribed circle to the circumscribed circle of an equilateral triangle is

Solution:

(d) PS. OT and RU are perpendiculars drawn from thevertices P, O and R, respectively.

∠ OQS=1/2∠ PQR=30°

Now in AOQS,

sin 30° ={OS}/{OQ}=\text"radius of the inner circle (r_1)"/\text"radius of the outer circle (r_2)"

⇒

1/2={r_1}/{r_2}

We have.

\text"Area of the inscribed circle"/\text"Area of the circumscribed circle"={πr_1^2}/{πr_2^2}

⇒

[{r_1}/{r_2}]=[1/2]^2=1:4

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