Question

METAL AND FANNED
Question: http://prntscr.com/3a12gi
Picture:
http://prntscr.com/3a170b

It also says
http://i.imgur.com/qtxeWY4.png

Answer 1

What kind of angle is angle PAO?

Answer 2

Not sure. I got 25

Answer 3

That is correct, but you can't find that without knowing about angles PAO and PBO.

Answer 4

Here's an explanation. In the third figure, you are told that rays PA and PB are tangent to the circle.

Answer 5

A tangent to a circle is perpendicular to the radius drawn to the point of tangency.

Answer 6

In the figure above, PA is a tangent to circle O. PA intersects the circle at point A. That means PA and OA are perpendicular, and angle OAP is a right angle.

Answer 7

Now look at your problem.
PA and PB are tangent to circle O.
That means angle OAP and OBP are right angles.

Answer 8

Two tangents drawn from a point to a circle are congruent.
That means segments PA and PB are congruent.
Since ray PD bisect angle BPA, angles APO and BPO are congruent.
Also, angles OAP and OBP are both right angles, so they are congruent.
That means that by ASA, triangles AOP and BOP are congruent.

Answer 9

So I was right that it was 25?

Answer 10

Since corresponding parts are congruent, angles BPO and APO are congruent.
Now we find the measure of angle APO.
m<APO + m<AOC + m<OAP = 180
m<APO + 65 + 90 = 180
m<APO = 25
m<BPO = m<APO = 25

Yes, you were correct.

Answer 11

wow thank you so much help

Answer 12

You're welcome.