## anonymous one year ago The measure of arc AXB is 196. What is the measure of the tangent-chord angle ABC? http://media.apexlearning.com/Images/200701/18/55e3ff85-2144-4d69-9c27-2b7789a8d76c.gif

1. anonymous

i reaalllyyyyy need the help :) please

2. welshfella

the m<ABC will be equal to the measure of the angle subtended by the chord in the opposite segment

3. welshfella

|dw:1434905469876:dw|

4. welshfella

you can use the fact that the arc AXB = 196 degrees to find the value of this angle

5. anonymous

is there a formula i can plug this into?

6. welshfella

I never did arcs when in college (many years ago) so i'm not sure!. Sorry you'll have to google that - or someone else probably knows

7. welshfella

there's probably a theorem

8. welshfella

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9. welshfella

the angle marked is 360 - 196 = 164 degrees

10. welshfella

this is the angle at the center of the circle

11. anonymous

then do you subtract it from 180 and with that answer divide by 2?

12. welshfella

|dw:1434906331031:dw|

13. welshfella

that angle is 82 because its 1/2 of 164

14. welshfella

now opposite angles of a cyclic quadrilateral add up to 180 so the opposite angle = 180 - 82 = 98

15. Mertsj

The Theorem: An Angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc. 1/2 of196=98

16. welshfella

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17. welshfella

- which makes m<ABC = 98 degrees this might be a round about way to do it though!!

18. anonymous

thank you !

19. anonymous

could you help me with another one?

20. welshfella

there you go Mertsj has a quick way

21. anonymous

If the measure of angle DEF is 65, what is the measure of arc DE ? http://media.apexlearning.com/Images/200701/18/df4742e6-e568-423e-bfe0-61f1985506e7.gif

22. Mertsj

Did you read the theorem I posted above?

23. anonymous

so do i just double 65

24. welshfella

use the theorem Mertsj quoted

25. Mertsj

yes

26. anonymous

thank you!

27. Mertsj

yw

28. welshfella

easy using that theorem

29. Mertsj

yep. That's what theorems are for. You prove something once and for all and then you don't have to reinvent the wheel for every similar problem.

30. welshfella

true - Its weird but we never touched arc measurements in Geometry in the UK - as I said I'm talking decades ago. Maybe they do now.

31. Mertsj

hopefully

32. welshfella

yes - i don't understand why they didn't

33. anonymous

34. welshfella

lol - this is a learning experience for me - OK

35. anonymous

In the diagram below, line AB and BC and are tangent to center O. What is the measure of arc ADC?

36. anonymous

so sorry

37. anonymous
38. welshfella

well as a full circle is 360 degrees arc ADC = 360 - 140

39. anonymous

so its 220

40. welshfella

yes

41. anonymous

thank you so much seriously!

42. welshfella

yw

43. welshfella

i learned something new myself