iran-konkur 2016 Q125

iran-konkur · Other · konkur-riazi_1395_specialized Circles Circle-Line Intersection and Point Conditions
125. In a square with side 2 units, a circle with center at one vertex and radius $2.5$ units cuts two sides of the square. What is the distance from the nearest vertex of the square to the intersection points?
(1) $\dfrac{1}{\mathfrak{f}}$ (2) $\dfrac{1}{\mathfrak{r}}$ (3) $\dfrac{\sqrt{\mathfrak{r}}}{\mathfrak{r}}$ (4) $\dfrac{\sqrt{\mathfrak{r}}}{\mathfrak{r}}$
\textbf{125.} In a square with side 2 units, a circle with center at one vertex and radius $2.5$ units cuts two sides of the square. What is the distance from the nearest vertex of the square to the intersection points?

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(1) $\dfrac{1}{\mathfrak{f}}$ \hfill (2) $\dfrac{1}{\mathfrak{r}}$ \hfill (3) $\dfrac{\sqrt{\mathfrak{r}}}{\mathfrak{r}}$ \hfill (4) $\dfrac{\sqrt{\mathfrak{r}}}{\mathfrak{r}}$

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