PLEASE HELP ME!!!Omar is constructing a square inscribed in a circle. He begins by constructing a circle with a center O and wit
h a diameter connecting points A and C .
What is Omar's next step in the construction?
A
Starting at point A , use the compass with a setting of the length of the radius to mark off the radius four times around the circle.
B
Use OA¯¯¯¯¯ to construct a line tangent to the circle at point A .
C
Construct a perpendicular bisector of AC¯¯¯¯¯ , making it long enough to touch the circle above and below the diameter.
D
Construct a perpendicular bisector of OC¯¯¯¯¯ , making it long enough to touch the circle above and below the diameter.
What is Omar's next step in the construction?
A
Starting at point A , use the compass with a setting of the length of the radius to mark off the radius four times around the circle.
B
Use OA¯¯¯¯¯ to construct a line tangent to the circle at point A .
C
Construct a perpendicular bisector of AC¯¯¯¯¯ , making it long enough to touch the circle above and below the diameter.
D
Construct a perpendicular bisector of OC¯¯¯¯¯ , making it long enough to touch the circle above and below the diameter.
1 answer:
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<h3>Answer: Choice D. 
</h3>
The red angle markers show those two angles are congruent. That's one "A" of "ASA". The S refers to a congruent pair of sides. We don't have any tickmarks to indicate congruent pairs; however, we do know that QR = QR is a shared side that overlaps (reflexive theorem). So this is the "S" in "ASA".
The thing missing is the angle Q of the top triangle, and also of the bottom triangle as well. If we know those two angles are congruent, then we have enough info to use ASA. More specifically, if we know that , then we can use ASA.
One thing to notice is that the other answer choices involve side lengths and not angles. This implies that if A, B or C were one of the answers, then we would have something like SAS or SSS. But instead we want ASA. So we can immediately rule choices A,B, and C out.