## Proving angles are equal in a triangle in a circle.

For the discussion of math. Duh.

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markosheehan
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### Proving angles are equal in a triangle in a circle.

hi can someone help me work this out. i think it has something to do with the exterior angle of a triangle is equal to the sum of the interior angles but i cant work it.

Qaanol
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### Re: Proving angles are equal in a triangle in a circle.

The problem is asking you to prove that two lengths are equal.

Is this homework?
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### Re: Proving angles are equal in a triangle in a circle.

Literally a photo of a math textbook.
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Tub
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### Re: Proving angles are equal in a triangle in a circle.

To solve this, you need to know only two things:
* the sum of the inner angles of triangles
* a tangent forms a 90° angle to the radius.

Given just that information, every relevant angle of the triangle can be expressed in terms of the blue angle. But something important is missing from the diagram, something that every circle must have..

Flumble
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### Re: Proving angles are equal in a triangle in a circle.

Tub wrote:But something important is missing from the diagram, something that every circle must have..

A hat?

markosheehan
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### Re: Proving angles are equal in a triangle in a circle.

its center point?

doogly
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### Re: Proving angles are equal in a triangle in a circle.

Yup. You should draw it yourself, pick a name for it (maybe O, for Origin, D, for Doug, something like this) and start using it for some calculations.

It turns out this is a leap that is often quite tricky for students -
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Soupspoon
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### Re: Proving angles are equal in a triangle in a circle.

Flumble wrote:
Tub wrote:But something important is missing from the diagram, something that every circle must have..

A hat?

A brooch? A pterodactyl?

Zohar
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### Re: Proving angles are equal in a triangle in a circle.

To be fair, it's not explicitly stated AT is a tangent to the circle in the drawing, is it?
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doogly
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### Re: Proving angles are equal in a triangle in a circle.

But they use a T! T is for tangent.
(But yes, generally that is the sort of thing people spell out in these questions.)
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?

Tub
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### Re: Proving angles are equal in a triangle in a circle.

Zohar wrote:To be fair, it's not explicitly stated AT is a tangent to the circle in the drawing, is it?

It's not explicitly stated that the round thing is a circle, either. Sometimes, you just got to have faith.

Zohar
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### Re: Proving angles are equal in a triangle in a circle.

I would have expect to see "AT is a tangent to the circle O" in there, which would have solved both those problems.
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Cauchy
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### Re: Proving angles are equal in a triangle in a circle.

I don't really understand why people are saying to add the center, or construct right angles, or what have you.

In terms of circle arc measures, what is the measure of angle TAC? What is the measure of angle ABC? You should have theorems about both of these.
(∫|p|2)(∫|q|2) ≥ (∫|pq|)2
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doogly
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### Re: Proving angles are equal in a triangle in a circle.

You can't just "have theorems." That's a kind of cheating. You have to draw things.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?

Demki
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### Re: Proving angles are equal in a triangle in a circle.

doogly wrote:You can't just "have theorems." That's a kind of cheating. You have to draw things.

You also have to locate the center with just an unmarked straight edge

doogly
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### Re: Proving angles are equal in a triangle in a circle.

It doesn't have to be constructed, just declared.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?