## OpenSessame 2 years ago In circle O, PA and PB are tangents. a. Prove APO = BPO . b. Find m BOD for m AOP = 64. Explain your reasoning.

1. OpenSessame

2. OpenSessame

@Directrix

3. Directrix

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

4. OpenSessame

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

5. OpenSessame

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

6. Directrix

First, the marked up diagram.

7. Directrix

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

8. OpenSessame

OKay!

9. OpenSessame

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.

10. Directrix

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

11. Directrix

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.

12. OpenSessame

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

13. Directrix

How about those reasons - you have more to do.

14. OpenSessame

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

15. Directrix

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.

16. OpenSessame

Ugh:( I hate Geometry lol...

17. Directrix

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.

18. Directrix

You're up for part 2.

19. OpenSessame

For part two...

20. OpenSessame

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.

21. Directrix

I think 116 is correct.

22. OpenSessame

Okay :)

23. Directrix

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.

24. OpenSessame

im studing for the final so like everything...

25. OpenSessame

Tmrw...