Question

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:

What is the measure of angle ACB?

32°
6°
24°
12°

Answer 1

@snowflake0531

Answer 2

@AZ

Answer 3

Here's the theorem

Answer 4

so we're looking for angle ACB

ACB = 1/2 * (AB - AX)

We know AB is 152

but we have to first find AX so we can find the angle

Answer 5

You have to use this formula to calculate AX

the inscribed angle is half the arc

Answer 6

btw I'm pulling these screenshots from https://mathbitsnotebook.com/Geometry/Circles/CRAngles.html

Answer 7

Eek sorry for responding so late got carried away, so how exactly do you use the formula?

Answer 8

So to first find AX

the angle is 64

the arc is AX

64 = 1/2 * AX

what is AX = ??

Answer 9

the measure of angle abc is one half the measure of the distance along the circle from point a to point c

Answer 10

hope my explination of the previous formula is correct if not someone please correct me

Answer 11

128..?

Answer 12

is that what you have come up with

Answer 13

its probably right

Answer 14

AZ? Is that right?

Answer 15

yes, that's the value of AX

so now we can find the value of the angle ACB

Answer 16

Look at that first image I attached

We know that

ACB = 1/2 * (AB - AX)

from the image
AB = 152

and we calculated AX = 128

so can you plug it in

Answer 17

Yes we first need to plug it in.

Answer 18

ACB = 1/2 * (152 - 128)

ACB = ??

Answer 19

Uh is it 12? Sorry if I'm wrong

Answer 20

That's correct

Answer 21

Oh awesome