In the given equilateral triangle, the smaller circle and the bigger semi circle

Question

In the given equilateral triangle, the smaller circle and the bigger semi circle are inscribed inside. What is the value of

\frac{X}{Y}

Answer: Option A
:
A
Line PV bisects line QR.

Δ

PST and

Δ

TUV are similar.
Hence

\frac{Z}{Y + X} = \frac{Y}{X = Y}; \Rightarrow \frac{Y}{Z} = \frac{X - Y}{X + Y};

but in

Δ

PST,

\frac{Y}{Z}

= sin 30 =

\frac{1}{2}

Hence

(\frac{1}{2})

\frac{X - Y}{X + Y}; \Rightarrow \frac{X}{Y} = 3

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