In a circle AD and CD are diameters. Which of the following must be true?
I. The length of arc ABD is equal to the length of arc BAC.
II. AB is perpendicular to CD.
III. ABCD is a square.
Aside from how to solve this problem, I also dont understand how they are getting arc ABD and BAC since I thought you read arcs in order? Thanks!
Unless you typed incorrectly, doesn’t this mean that A and C are at the same point? Do you mean AB, CD?
In that case, I must be true; II and III need not be true.
Arc XYZ on a circle refers to the arc whose endpoints are X, Z and passes through point Y.
Srry yes. It is AB and CD that are diameters
Would you also mind explaining how you arrived at your conclusion that I. is the only answer? Also counterexamples disproving II and III would be great
Draw it out.
I:
length of arc ABD = length of arc AB + length of arc BD
length of arc BAC = length of arc BA + length of arc AC
Arcs BD and AC are equal in length (this has to do with the fact that AB, CD are diameters), and arc AB (or arc BA) is just a diameter. So arc ABD = arc BAC in terms of length.
II, III: Draw two diameters of the circle (labelled AB, CD) that intersect but not at a right angle. This should easily disprove both II and III.
where did you find this problem?
SAT June 2014 released test
I dont know Marsha. It was a released test. I guess it wasn’t June then…