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Poster has been reminded to use the HH Template and show their work

## Homework Statement

write the proof

## Homework Equations

none

## The Attempt at a Solution

I've tried 5 times, got nowhere

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- Thread starter Ameer Bux
- Start date

- #1

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Poster has been reminded to use the HH Template and show their work

write the proof

none

I've tried 5 times, got nowhere

- #2

Buzz Bloom

Gold Member

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Problem 7 is tricky because the figure is not drawn in a manner consistent with the statements about it. You might find it helpful to redraw it so that SB is a diameter of the circle ABC. At least that's how I interpret the text:"SB bisects ABC."

Problem 8 is easier. I suggest you look up

Read about proposition 1.32.

Hope this helps.

Regards,

Buzz

- #3

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What do the numbers (1&2) in the diagram indicate? Are all angles labeled 1 supposed to be equal?

- #4

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I think it might mean that line SB bisects angle OBC. Here's a picture drawn to scale assuming that:Hi Ameer Bux:

Problem 7 is tricky because the figure is not drawn in a manner consistent with the statements about it. You might find it helpful to redraw it so that SB is a diameter of the circle ABC. At least that's how I interpret the text:"SB bisects ABC."

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- #5

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- #6

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What do the numbers (1&2) in the diagram indicate? Are all angles labeled 1 supposed to be equal?

Ameer appears to have disappeared, which is annoying enough. But to answer your question, looking at his second picture, I think when he as a 1 and 2 at vertex A that it is a very awkward notation where it would have been much better to call them A1 and A2. Similarly the 1 and 2 at vertex R refer to angles better notated as R1 and R2. So all those 1's and 2's are different. Awful notation in his pictures.

- #7

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Buzz, do you have an argument for problem 8? I don't see it and I have my doubts it is even true. And I don't see proposition 1.32 at that link. ??Problem 8 is easier. I suggest you look up

Read about proposition 1.32.

Hope this helps.

Regards,

Buzz

- #8

Buzz Bloom

Gold Member

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Hi LCKurtz:Buzz, do you have an argument for problem 8?

Thank you for noting my error. Somehow I read the handwritten question as referring to R

From the link:And I don't see proposition 1.32 at that link. ??

... the term "exterior angle theorem" has been applied to a different result,[1] namely the portion of Proposition 1.32 which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

Regards,

Buzz

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- #10

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Maybe I am missing something but it looks quite easy.

I sent details to Buzz in a private conversation, but for some reason it would not let me add you as a recipient. You must be in a higher astral plane. I thought it premature to post what might be a solution to the thread.

@Ameer Bux , what do you know about opposite angles of a quadrilateral whose vertices lie on a circle?

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For the first problem, the theorem which states that equal arcs subtend equal angles on a circle is applicable.## Homework Statement

write the proof

## Homework Equations

none

## The Attempt at a Solution

I've tried 5 times, got nowhere

- #12

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- #13

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I really have to learn geometry. I look foolish with a math degree without knowing geometryFor the first problem, the theorem which states that equal arcs subtend equal angles on a circle is applicable.

- #14

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You mean like what was mentioned in post #5?For the first problem, the theorem which states that equal arcs subtend equal angles on a circle is applicable.

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Yes, I see you had already mentioned it.You mean like what was mentioned in post #5?

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