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

- anonymous

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- anonymous

i reaalllyyyyy need the help :) please

- welshfella

the m

- welshfella

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## More answers

- welshfella

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

- anonymous

is there a formula i can plug this into?

- 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

- welshfella

there's probably a theorem

- welshfella

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- welshfella

the angle marked is 360 - 196 = 164 degrees

- welshfella

this is the angle at the center of the circle

- anonymous

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

- welshfella

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- welshfella

that angle is 82 because its 1/2 of 164

- welshfella

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

- 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

- welshfella

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- welshfella

- which makes m

- anonymous

thank you !

- anonymous

could you help me with another one?

- welshfella

there you go Mertsj has a quick way

- 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

- Mertsj

Did you read the theorem I posted above?

- anonymous

so do i just double 65

- welshfella

use the theorem Mertsj quoted

- Mertsj

yes

- anonymous

thank you!

- Mertsj

yw

- welshfella

easy using that theorem

- 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.

- 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.

- Mertsj

hopefully

- welshfella

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

- anonymous

how about another one?

- welshfella

lol - this is a learning experience for me - OK

- anonymous

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

- anonymous

so sorry

- anonymous

http://media.apexlearning.com/Images/200701/18/ac3f47ed-9e85-4bd0-a3dc-1b67c4cc90fb.gif

- welshfella

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

- anonymous

so its 220

- welshfella

yes

- anonymous

thank you so much seriously!

- welshfella

yw

- welshfella

i learned something new myself

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