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:

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 152 degrees, and angle CBA measures 64 degrees.

What is the measure of angle ACB?

32°
6°
24°
12°

Answer 1

Help pls

Answer 2

Just wanted a picture to help me think through it. Just a moment please

Answer 3

Sorry, I missed some important info in my last drawing. We know CBA is 64 degrees. We also know that line CA draws a tangent to the circle, which forms a 90 degree angle with the radius of the circle. And I redrew the 152 degree measure to be less confusing.
From my (admittedly bad) drawing, I'm leaning toward 24 degrees, but I have to say I'm not entirely confident about that. I still think there's something I'm missing...

Answer 4

Say, I don't suppose you have a figure to go with the question, do you? It'd definitely be more helpful than my crummy drawing! :)

Answer 5

Here is the image: https://snipboard.io/tWGAac.jpg

Answer 6

Sorry buddy, I have to be able to admit when I'm stumped. It's been a while since I've done a problem like this, and the solution isn't really jumping out at me. Should we try asking someone else?

Answer 7

WAIT I think I got it

Answer 8

It's all good

Answer 9

rA and rB (radius to those points) are equal lengths, so rAB and rBA will have equal angle measures.
That means rAB is (180 -152)/2 = 14
And that means that BAC is 90 + 14 = 104
And THAT means that BCA is 180 - (104+64) or 180 - 168 = 12

Answer 10

Yessssssssssssss thank you so much

Answer 11

Not at all, it's kind of fun puzzling these things out, if a little bit frustrating :)