Question

PLEASE HELP!!!!


The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X.

The figure shows a circle with points A and B on it and point C outside it. Side BC of triangle ABC intersects the circle at point X. A tangent to the circle at point A is drawn from point C. Arc AB measures 156 degrees and angle CBA measures 32 degrees.

What is the measure of angle ACB?

23°

32°

46°

16°

Answer 1

Are you familiar with any secant tangent circle theorems?

Answer 2

If not, then check out this page

http://www.mathwarehouse.com/geometry/circle/tangents-secants-arcs-angles.php


In this problem, you'll be using the third formula (the one on the very right)

Answer 3

Let me know if it helps or not

Answer 4

hey:) ..ok im lookin at it bc i cant remember the theorem

Answer 5

alright, let me know if it makes sense or not

Answer 6

im still confused what do i do??

Answer 7

basically, you need to find the measures of arcs of AB and AX. Luckily, AB is given as 156, so you just need to find arc AX

Answer 8

how do we find the measure of arc AX?

Answer 9

umm im not sure!:/

Answer 10

alright, do you see the angle ABX?

Answer 11

yes!

Answer 12

what is the measure of that angle

Answer 13

32?

Answer 14

good

Answer 15

notice how the angle ABX cuts off the circle to form arc AX, do you see this?

Answer 16

yes i do:)

Answer 17

Good

Now let's call the center point O. By the inscribed angle theorem, we can say


AOX = 2*ABX


So

AOX = 2*ABX

AOX = 2*32

AOX = 64


This means that the central angle AOX is 64 degrees. Therefore, the arc AX is 64 degrees.

Answer 18

Now use the formula on that page I gave you


C = (1/2)*(AB - AX)

C = (1/2)*(156 - 64)

C = 46


So in the end, the angle C is 46 degrees. So angle ACB = 46

Answer 19

That's great

Answer 20

thank you ur awesome:)

Answer 21

you're welcome