Question

Please please please help me with this given graph. there's a couple questions. I really need help with this
GIVEN:
PB tangent
PV, PU secants

If m VU= 80° and m ST= 40°, then ∠1 =
If m VU= 70° and m ST= 30°, then ∠2 =
If m VB= 60° and m BS = 30°, then ∠3 =
If VS = 9, SP = 12 and UT = 4, then TP =

https://media.glynlyon.com/g_geo_2012/11/pg43art2.gif

Answer 1

http://www.regentsprep.org/Regents/math/geometry/GP15/CircleAngles.htm

Answer 2

doesnt help =/

Answer 3

does If m VU= 80° and m ST= 40°, then ∠1 = ...60???
If m VU= 70° and m ST= 30°, then ∠2 = .... 35?
If m VB= 60° and m BS = 30°, then ∠3 =... 15?
If VS = 9, SP = 12 and UT = 4, then TP = ...18?

Answer 4

∠1 = (80° - 40°)/2 = 40°/2 = 20°

Answer 5

are the others correct?

Answer 6

∠2 = (60° + 30°)/2 = 90°/2 = 45°

Answer 7

∠3 = (60° - 30°)/2 = 30°/2 = 15° (you are right)

Answer 8

I am confused.
∠1 = 20?
∠2 = 45? I don't think thats right <<

Answer 9

read the site which i posted, the 2nd part figure is useful to solve ∠1

Answer 10

i mean the last 2nd part figure

Answer 11

If m VU= 80° and m ST= 40°, then ∠1 = 40?
If m VU= 70° and m ST= 30°, then ∠2 = 20?

Answer 12

∠1 = 40/2 = 20 (because ∠1 is formed by two secants intersecting " outside " of circle, then use the formula :
∠1 = (arc VU - arc ST)/2

Answer 13

Thank you :)

Answer 14

what about that last one, does it equal 18?
VS = 9, SP = 12 and UT = 4, then TP =?

Answer 15

use this proportion :

TP/UP = SP/VP, (notice that UP = UT + TP, and VP = VS+SP)
TP/(UT + TP) = SP/(VS + SP)
TP/(4+TP) = 12/(9+12)
TP/(4+TP) = 12/21
TP/(4+TP) = 4/7
cross multiply, we get
7 TP = 16 + 4 TP
7 TP - 4 TP = 16
3TP = 16
TP = 16/3 = 5.33

does that make sense ?

Answer 16

Kinda.

Answer 17

http://www.regentsprep.org/Regents/math/geometry/GP14/CircleSegments.htm

Answer 18

i used theorem 2 above