Please teach me how to find the measurements in this circle?

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Is arc AD 200? since the inscribed angle is half the arc?
 

Dr.Peterson

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Is arc AD 200? since the inscribed angle is half the arc?
No. The marked 100 degree angle AOD is not an inscribed angle, but a central angle; so arc AD has measure 100 degrees.

I would mark the other three central angles (at O) and use those to find the arcs in the same way.

Then I would find the inscribed angles, such as DAC.

Then angle AED is different; you might think about quadrilateral AEDO. What are the angles at A and D? Or you might have a theorem you can apply directly.
 
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No. The marked 100 degree angle AOD is not an inscribed angle, but a central angle; so arc AD has measure 100 degrees.

I would mark the other three central angles (at O) and use those to find the arcs in the same way.

Then I would find the inscribed angles, such as DAC.

Then angle AED is different; you might think about quadrilateral AEDO. What are the angles at A and D? Or you might have a theorem you can apply directly.
the arc will have the same measure as a central angle? does that mean all the angles in the center have the same measurement as arcs?

I think
angle BOC will be 100,
angle AOB will be 80
angle DOC will be 80?
does it make the arcs across from it the same?

The inscribed angle DAC will be 40 since arc DC is 80.

quadrilateral had to equal 360,
and angle A and D are congruent
angle A and D are 40?
40+40+100+180 = 360
angle AED = 180?


arc AD = 100
arc DC = 80
arc AB = 80
angle DAC = 40
arc ACD = 260
angle ACB = 40
angle AED = 180
arc ADC = 180
 

Dr.Peterson

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Joined
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Messages
11,107
the arc will have the same measure as a central angle? does that mean all the angles in the center have the same measurement as arcs?
Yes.

angle BOC will be 100,
angle AOB will be 80
angle DOC will be 80?
does it make the arcs across from it the same?
Yes.

The inscribed angle DAC will be 40 since arc DC is 80.
Yes.

quadrilateral had to equal 360,
and angle A and D are congruent
angle A and D are 40?
40+40+100+180 = 360
angle AED = 180?
Does it look like 180?? Can EAO and EAO possibly be 40 degrees?

What is true of an tangent and the radius?

arc AD = 100
arc DC = 80
arc AB = 80
angle DAC = 40
arc ACD = 260
angle ACB = 40
angle AED = 180
arc ADC = 180
Just fix AED.
 
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Yes.


Yes.


Yes.


Does it look like 180?? Can EAO and EAO possibly be 40 degrees?

What is true of an tangent and the radius?


Just fix AED.
ok, tangent and radius form a right angle?

so angle EAO and angle EDO will be 90?
AED = 80?
 

Dr.Peterson

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Messages
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ok, tangent and radius form a right angle?

so angle EAO and angle EDO will be 90?
AED = 80?
Correct. And in general, the angle between tangents is the supplement of the intercepted arc.
 
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Correct. And in general, the angle between tangents is the supplement of the intercepted arc.
Alright. Thank you for helping me. I understand it fully now.
 
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