In the diagram above, AB = 10 is the diameter of the circle, and AC =

Most geometry problems require the drawing of multiple possible figures to help figure out some key relationship that makes the question way easier. First, draw a triangle that extends far above the circle. clearly this is an acute triangle, therefore a triangle that connects below the circle will be obtuse, thus we can rely on Largest side^2 > sum of squares of other two sides.

In the diagram above if we extend BC to a point on the circle then since AB is the diameter and the extended portion (D) of BC on the circle would be a chord. In this case angle BDA would be 90 deg angle and hence as per Pythagoras theorem BD would be 8 .

Since BD would be an extension of BC hence BD should be less than 8. Hence 7.

If point C were on the circumference of the circle, then we know from the concept of Inscribed Angles in a semi-circle that the Angle would be 90 degrees.

Start out with Point C on the circumference. This is a 90 degree angle.

Then, to get to the figure, just picture “flattening” or “dragging down” point C closer to the diameter of the circle.


This will result in the Angle at Vertex C becoming wider.

The Side of Length 6 that would fit the right triangle (6-8-10) would have to stay the same, but in order to accommodate this wider angle, the unknown side would have to shorten.———-> hence, we would have an obtuse triangle with one angle greater then 90 degrees and the unknown side will have to be shorter than the Leg of length 8 were the angle actually 90 degrees

Any triangle that has one angle greater than 90 degrees (there can only ever be one angle that is greater than 90 degrees) is an obtuse triangle

Now that you know the triangle must be an obtuse triangle, you can use the Property that GMATinsight uses

For any obtuse triangle:

(Longest side)^2 > (shorter side)^2 + (other shorter side)^2


You end up with the inequality that the unknown side must be less than < 8

Only I



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