#28 of June 2015 Grade 10 CSAT(Korean SAT) Mock test

Geometry Level 4

As shown above, there is a regular triangle \(ABC\).

Let \(M\text{, }N\) be midpoints of \(\overline{AB}\) and \(\overline{AC}\).

\(\overrightarrow{MN}\) and the circumcircle of \(\triangle ABC\) intersect at point \(P\), which satisfies \(\overline{NP}=1\).

Define \(x=\overline{MN}\).

Find the value of \(10\left(x^2+\dfrac{1}{x^2}\right)\).

This problem is a part of <Grade 10 CSAT Mock test> series.


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