Question

mc002-1.jpg
O is the center of the circle. Assume that lines that appear to be tangent are tangent. What is the value of x?

Answer 1

can we also have a screenshot maybe?

Answer 2

http://phgeometryfinalexamreview.wikispaces.com/file/view/VERY_IMPORTANT.png/148266885/741x242/VERY_IMPORTANT.png

the picture there uses a secant and a tangent
but is pretty much the same thing really

all you'd need are the INTERCEPTED CENTRAL ANGLES

the central angle given there is 157 degrees
what do you think is the other arc's central angle is?

Answer 3

78.5?

Answer 4

well, look at the circle
keep in mind the circumference of the circle is 360 degrees

Answer 5

101.5?

Answer 6

well, the lines are touching the circle at the central angle of 157 degrees
so the other bigger central angle will be 360 - 157
the rest of 360 once 157 is subtracted from it

Answer 7

203

Answer 8

yes, so the angle of "x", of the outside intersecting tangents, will be \(\bf \cfrac{\textit{far arc - near arc}}{2}\)

Answer 9

203/2

Answer 10

you're forgetting the "near arc", which is given

Answer 11

so 203-157=46/2=23

Answer 12

yes, \(\bf x = 23^o\)

Answer 13

can you help me with another problem?

Answer 14

I can try :)

Answer 15

What is the value of x to the nearest tenth?

Answer 16

notice the line going across the circle is the diameter
so if one side is 16, the other side is also 16, thus the radius is 16

now look at the triangle, using pythagorean theorem, what do you think is the missing vertical leg/side?

\(\bf c^2 = a^2 + b^2 \implies c^2 - a^2 = b^2 \implies \sqrt{c^2-a^2} = b\)

Answer 17

I don't understand how to do that.

Answer 18

http://www.youtube.com/watch?v=AA6RfgP-AHU

Answer 19

then its 9.6