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?

a. 29°
b. 8°
c. 16°
d. 21°

Answer 1

First, consider <B, an inscribed angle of the circle. It has measure 42 so its intercepted arc XA has ? measure. Check out the attachment.

Answer 2

@lowcard2 intercepted arc XA has ? measure what

Answer 3

84 ?

Answer 4

Okay.

Answer 5

Now, look at <C outside the circle. It is an angle formed by a tangent segment and a secant segment drawn to a circle from an outside point. See attachment for its formula.

Answer 6

m<C = (1/2) ( 100 - 84)

m<C = ? @lowcard2

Answer 7

100 - 84 =16 /2
8?

Answer 8

That is what I got.