Hi Mission2012,

I'm going to "tweak" your sentence a bit, but I can tell you that the idea that you're talking about IS true.

When two lines that are tangent to a circle and perpendicular to one another, then the arc of the circle that exists between them will be 1/4 of the circumference.

GMAT assassins aren't born, they're made,
Rich

Mission2012 wrote:Is it true -

Only way two perpendicular lines can be tangent to the same circle if the arc they form represent exactly one quarter of a circle.

Dear Mission2012,
I happy to add my two cents.

Yes, this statement is true. For example, suppose the circle has a center O, the two tangents are tangent at points A & C, and the tangents intersect at point B outside of the circle. We already know angles A & C, where the radius meets a tangent, are 90 degree angles. If B is also a right angle, that's a quadrilateral with three right angles --- since the sum of the angles must be 360 degrees, then if three of the angles are right angles, the fourth must be a right angle also. In fact, because all the lengths are equal, quadrilateral OABC has to be a square.

This is a rare case in which a relatively simple specification guarantees the quadrilateral formed is a square. Normally, guaranteeing something is a square is not so easy. See:
https://magoosh.com/gmat/2012/gmat-geome ... -a-square/

Does all this make sense?
Mike