# #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.

×