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?

Answer 1

Can someone please help me.

Answer 2

@ryan123345 can you help me please?

Answer 3

@Mertsj this is the question I'm having trouble with. You think you could help

Answer 4

What is the measure of arc AX?

Answer 5

I don't know how to find the measure of the arc?

Answer 6

Do you know that angle B is an inscribed and its arc is arc AX?

Answer 7

Yeah I know that

Answer 8

And do you know that inscribed angles are half their arcs?

Answer 9

No what do you mean by that?

Answer 10

I mean if you multiply the inscribed angle by 2 you will have the measure of its intercepted arc.

Answer 11

Okay

Answer 12

So what is arc AX?

Answer 13

84

Answer 14

So now we need the theorem that says that an angle formed by a tangent and a secant that intersect outside the circle is 1/2 the difference of the intercepted arcs.

Answer 15

Can you apply that theorem?

Answer 16

I don't know that theorem but I know what the tangent and secant are

Answer 17

What are the measures of the two arcs intercepted by the tangent and the secant?

Answer 18

Do you mean the 100 and 84?

Answer 19

Yes. Those are the arc measures. What is the difference of those arcs?

Answer 20

16

Answer 21

What is 1/2 of 16?

Answer 22

8

Answer 23

That is the measure of angle ACB

Answer 24

that's all? Thanks

Answer 25

yw