This is a blog for my second semester pre-calculus 30s students. Have a blast!

Thursday, April 20, 2006

Circle Geo. pre-test answers

MC:

1) d 2) b 3) c 4) b 5) b 6) d 7) a 8) c 9) b 10) b

LA:

1) ABC is an impossible triangle, so no solution.

2) Using the pythagorean thm... OE = 4.9

3) vertex = (2, 4)
eq'n of line in std form: x - y = 0

distance = sqt(2) / 2

4) angle 5 = 45 deg (insc. angle subtented by same arc)

angle 1 = 180 - 45 - 75 = 60 deg

angle 2 = 35 deg (insc. angle subtended by same arc)

angle 4 = 180 - 45 - 60 - 35 = 40 deg (opp. angles of cyclic quad supp.)

angle 3 = 180 - 75 = 105 deg (opp. anles of cyclic quad supp.)


5) angle 1 = 15 deg (cong. triangles - SSS)

angle 2 = 180 - 15 - 90 = 75 deg (tang/chord thm)

angle 3 = 90 - 75 = 15 deg

angle 4 = 180 - 90 - 15 = 75 deg

angle 5 = 90 deg (tang/chord thm)


6) angle 2 = 180 deg (subtended by diam.)

arc AD = 60 deg

therefore...angle 1 = 110 / 2 = 55 deg (central / insc. angle subtended by same arc)

angle 3 = 60 / 2 = 30 deg (insc. angle subtended by same arc)

arc BC = 180 - 60 - 50 = 70 deg

therefore...angle 4 = 120 / 2 = 60 deg (insc. angle subtended by same arc)

angle 5 = 70 deg (cent. angle subtended by same diam.)


7) using pythagorean thm.... OD = 5.29 cm



BONUS:

3

4 Comments:

Blogger vincent said...

Mr M. uhhh.. I think some of these answers are wrong.. But maybe I'm wrong. I have different answers

for #5, I got letter C (131.8 degrees, 228.2 degrees)..

for #9, shouldn't it be letter A? since the vertex is (-4,6).

for Long Answer #3, shouldn't it be.. distance = root 2?

for LA #6, the angle subtended by the diameter forms a 90 degrees, not 180..

just asking for confirmation. thanx!

7:52 PM

 
Blogger tim-Math-y said...

This comment has been removed by a blog administrator.

9:28 PM

 
Blogger Mr. Malandrakis said...

You're right on these corrections Vince. My apologies as I was in a rush this afternoon and I used the answer key provided to me by the teacher that gave me this test. Thank you very much for your efforts.

9:29 PM

 
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