Question

In circle O, PA and PB are tangents.

a. Prove APO = BPO .
b. Find m BOD for m AOP = 64. Explain your reasoning.

Answer 1

@Directrix

Answer 2

Is this --> APO = BPO supposed to be △APO ≅ △BPO ?

Answer 3

Yes i didnt know how to write the triangle thing...

Answer 4

I know how to do B but a is were im confused...

Answer 5

First, the marked up diagram.

Answer 6

I'll do the statements; you do the reasons after I get the statements posted.

Answer 7

OKay!

Answer 8

Okay the first is given. and the second is a rule i cant but my finger on the name but says that if a circle has two tangents they are perpendicular.

Answer 9

1. Circle O with tangents PA and PB

2. Segment AO is perpendicular to Segment PA
Segment OB is perpendicular to Segment PB

3. △APO and △BPO are right triangles

4. PA = PB

5. PO = PO

6. △APO ≅ △BPO

---------
<POA ≅ <POB

Answer 10

1. Given
2. If a radius is drawn to a tangent to a circle at the point of tangency, the the radius is perpendicular to the tangent.
3.

Answer 11

Just saw that lol, three because they are tangents so they touch the other line at 90 degrees

Answer 12

How about those reasons - you have more to do.

Answer 13

Im seriously lost at theorems and things thats mainly what i need help with...

Answer 14

You'll need to study them and then to learn them. There's just no getting around that in Geometry. They come back after proofs in the form of problems to work.

Answer 15

Ugh:( I hate Geometry lol...

Answer 16

1. Given
2. If a radius is drawn to a tangent to a circle at the point of tangency, the the radius is perpendicular to the tangent.
3. Definition of right triangles.
4. Tangents drawn to a circle from an outside point are congruent.
5. Reflexive Property
6. HL (Hypotenuse Leg) Theorem

You'll need this for part two which you said you had done.

<POA ≅ <POB
Corresponding parts of congruent triangles are congruent.

Answer 17

You're up for part 2.

Answer 18

For part two...

Answer 19

Since AOP and AOB are congruent you can think of AOB as 64 too. Now these two angles make a straight line and a straight line is 180 degrees so the two angles added together must be 180.
180 – 64 = 116 degrees is <BOD.

Answer 20

I think 116 is correct.

Answer 21

Okay :)

Answer 22

I don't know which theorems your class has studied up until this point but I think the ones in the proof will be okay. After you study them more, then we can talk about their application. You obviously know many of them but are a little rusty on others. No big deal. Just make yourself study them.

Answer 23

im studing for the final so like everything...

Answer 24

Tmrw...