As a part of a geometry assignment, Andrew will construct a circle through three given points A, B, and C and then construct a tangent to the circle through point A. Andrew wrote down the steps he will use as shown below.

Step 1: Draw line segments AB and BC.
Step 2: Construct the perpendicular bisectors of segments AB and BC and label their point of intersection as O.
Step 3: Center the compass at point O and draw a circle through points A, B, and C.
Step 4: Draw the line OA and extend beyond the circle.
Step 5: Construct a perpendicular to the segment BC at point B.
Step 6: Draw the

Question

As a part of a geometry assignment, Andrew will construct a circle through three given points A, B, and C and then construct a tangent to the circle through point A. Andrew wrote down the steps he will use as shown below.
 
Step 1: Draw line segments AB and BC.
Step 2: Construct the perpendicular bisectors of segments AB and BC and label their point of intersection as O.
Step 3: Center the compass at point O and draw a circle through points A, B, and C.
Step 4: Draw the line OA and extend beyond the circle.
Step 5: Construct a perpendicular to the segment BC at point B.
Step 6: Draw the

anonymous · Answer

heres the rest....
tangent line through point A.
 
Which of these describes an error in the steps he will use to construct the circle and tangent?
Answer
		
Step 2 is incorrect. Construct the angle bisectors.
		
Step 3 is incorrect. Center the compass at point A and draw a circle through points O, B, and C.
		
Step 4 is incorrect. Draw the radius OA.
		
Step 5 is incorrect. The perpendicular should be constructed to segment OA at point A.

jim_thompson5910 · Answer

which one do you think it is?

anonymous · Answer

step 4? bcause that would go through the center and they asked for the tangent...

jim_thompson5910 · Answer

OA goes through the center, but OA is NOT the tangent line. It's merely constructed to help find the tangent line. The tangent line will be perpendicular to OA

jim_thompson5910 · Answer

So step 4 is actually a valid and useful step

jim_thompson5910 · Answer

which point do we want the tangent line to go through?

anonymous · Answer

so step 2 then? because the line perpendicular to OA helps construct the tangent

jim_thompson5910 · Answer

no, step 2 is useful for finding the center of the circle

jim_thompson5910 · Answer

so step 2 is also valid

anonymous · Answer

-___- is it  step 5 then because step three helps construct the circle its self

jim_thompson5910 · Answer

yes, it's step 5 because step 5 creates a perpendicular line to BC through point B, which is completely removed from point A, so this step has no meaning whatsoever

The correct thing to do construct a perpendicular line to OA through point A to create the tangent line that goes through A

anonymous · Answer

ok thank-you!!

jim_thompson5910 · Answer

you're welcome

anonymous · Answer

step 5