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 176 degrees and angle CBA measures 56 degrees.

What is the measure of angle ACB?

Answer 1

Look at the attached graphic.

Answer 2

So it should be (56+176)/2=Angle ACB?

Answer 3

I got 74?

Answer 4

I should probably say the choices are
32
60
28
16

Answer 5

@Directrix ?

Answer 6

Sorry, I am having problems posting.

The answer is not The measure of angle C = (1/2) * (176 - 28).

Just a second.

Answer 7

The near arc is 112. The inscribed angle is half that arc. The inscribed angle is 56 so the near arc is twice that or 112.

Answer 8

The measure of angle C = (1/2) * (176 - 112) = ? @_HoneyLemon_

Answer 9

Let me know what you get, okay. It should be one of the options.

Answer 10

32?

Answer 11

Yes, that is what I got.

It is the inscribed angle bad calculation that threw us off at the start. Sorry.

Answer 12

It's the first option

Answer 13

Yes, 32.

Answer 14

Thanks for your help :)

Answer 15

You are welcome.