Proving angles are equal in a triangle in a circle.

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

Postby markosheehan » Sun Oct 16, 2016 1:07 pm UTC

IMG_20161016_123255.jpg



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.

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

Postby Qaanol » Sun Oct 16, 2016 2:13 pm UTC

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.

Postby Weeks » Sun Oct 16, 2016 3:19 pm UTC

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

Postby Tub » Sun Oct 16, 2016 3:55 pm UTC

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..

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

Postby Flumble » Sun Oct 16, 2016 5:58 pm UTC

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

A hat?

hat.jpg

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

Postby markosheehan » Sun Oct 16, 2016 6:17 pm UTC

its center point?

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

Postby doogly » Sun Oct 16, 2016 8:23 pm UTC

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

Postby Soupspoon » Sun Oct 16, 2016 9:11 pm UTC

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

A hat?

A brooch? A pterodactyl?

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

Postby Zohar » Mon Oct 17, 2016 12:48 pm UTC

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

Postby doogly » Mon Oct 17, 2016 2:08 pm UTC

But they use a T! T is for tangent.
(But yes, generally that is the sort of thing people spell out in these questions.)
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Re: Proving angles are equal in a triangle in a circle.

Postby Tub » Mon Oct 17, 2016 2:23 pm UTC

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.

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

Postby Zohar » Mon Oct 17, 2016 2:25 pm UTC

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

Postby Cauchy » Mon Oct 17, 2016 5:59 pm UTC

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

Postby doogly » Mon Oct 17, 2016 7:47 pm UTC

You can't just "have theorems." That's a kind of cheating. You have to draw things.
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Re: Proving angles are equal in a triangle in a circle.

Postby Demki » Mon Oct 17, 2016 9:42 pm UTC

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

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

Postby doogly » Tue Oct 18, 2016 1:22 am UTC

It doesn't have to be constructed, just declared.
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