Question: If a circle passes through points (1, 2) (2, 5), and (5, 4), what is the diameter of the circle?

1. \(\sqrt{18}\)
2. \(\sqrt{20}\)
3. \(\sqrt{22}\)
4. \(\sqrt{26}\)
5. \(\sqrt{30}\)

Correct Answer: B

Approach Solution (1):

Look at the diagram below:

Calculate the lengths of the sides of the triangle ABC:

AB = \(\sqrt{10}\) ;
BC = \(\sqrt{10}\) ;
AC =\(\sqrt{20}=\sqrt2*\sqrt{10}\);

As we see the ratio of the ides of triangle ABC is 1 : 1 : \(\sqrt2\) , so ABC is \(45^\circ-45^\circ-90^\circ\) right triangle (in \(45^\circ-45^\circ-90^\circ\) right triangle the sides are always in the ratio 1 : 1 :\(\sqrt2\) )
So, we have right triangle ABC inscribed in the circle. Now, a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle
So AC = diameter =\(\sqrt{20}\)

“If a circle passes through points (1, 2) (2, 5), and (5, 4), what is the diameter of the circle?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills.

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