Question

The measure of AXB is 234. What is the measure of the tangent-chord angle ABC ?

Answer 1

let O be the center of circle.

Answer 2

first, find \(\angle OBA\)

Answer 3

How would i find that -__ - ?

Answer 4

There's no O ?

Answer 5

Oh i get what you mean, O represents the center of the circle.

Answer 6

Yes. draw it you will see how to find \(\angle OBA\)

Answer 7

Ignore the double o

Answer 8

It was only suppose to be one -__ -

Answer 9

63, because a circle is 360 degrees and i still need the degrees from the tangent-chord

Answer 10

let me show u

Answer 11

Okay

Answer 12

that angle at the center would be 126

Answer 13

That equals 360 so what would be left for the outside segment ?

Answer 14

Also i don't know how you got 126

Answer 15

126 = 360-234

Answer 16

minor arc = 360-major arc

Answer 17

I got that but i thought i needed to divide it since the tangent-chord was left -__ -

Answer 18

lets go step by step

Answer 19

radius and tangent make 90 degree angles. so that angle is 90

Answer 20

find <OBA and add it to 90. thats the reqiured angle ABC

Answer 21

So everything time i look for a tangent-chord i add up what i find as the radius by 90 then

Answer 22

Yes its 90 + that angle

Answer 23

<ABC = 450

Answer 24

how did u get that... no angle can be greater than 360

Answer 25

<ABC = 90 + 27 = 117

Answer 26

Didn't you mean that i add up the 126 + 234 and then add 90 or did you just mean 126 + 90?

Answer 27

nope look at the pic

Answer 28

stare at it for some time.

Answer 29

Just to be clear you did this 180 - 126 = 54/2 = 27 ?

Answer 30

Yes

Answer 31

Got it.

Answer 32

great ! we take half of 54 cuz, the triangle over there is isosceles. the base angles are equal, so each equal to half of 54