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Circle Geometry (1 Viewer)

taggs-sasuke

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I'll try posting here but if I don't get any replies, I'll post a new thread.

Well, I have more Circle Geometry questions... :(

I'll ask one question at a time so it won't turn you guys off.

Two circles are drawn with centres O and H. A line ACDB is drawn perpendicular to OH, cutting the circles at A, B and C, D respectively (i.e. it is not the common chord). Prove AC = BD.

Thanks guys! :)
 
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kurt.physics

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I'll try posting here but if I don't get any replies, I'll post a new thread.

Well, I have more Circle Geometry questions... :(

I'll ask one question at a time so it won't turn you guys off.

Two circles are drawn with centres O and H. A line ACDB is drawn perpendicular to OH, cutting the circles at A, B and C, D respectively (i.e. it is not the common chord). Prove AC = BD.

Thanks guys! :)



(This is the diagram)




































 
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taggs-sasuke

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More please :p
Hahaha.

Next question:

Two equal circles intersect in P and Q. A chord APB is drawn through P parallel to the line joining the centres O and H and meeting the circles in A and B. From O and H perpendiculars OX and HY are drawn to AB.

a. Prove OH = XY. What is true about OH and AB?

b. Prove OX = HY and also that the chords AP and PB are equal.

Thanks!
 

taggs-sasuke

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I'm going to go against my word but that's only because I really need help with Circle Geometry...

Anyway:

AB and DC are chords of a circle which meet when produced at X. The centre of the circle is O. If angleAOB = 110, angleXBC = 68 and angleXCB = 80, find angleCOD.

Thanks!
 

kurt.physics

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Hahaha.

Next question:

Two equal circles intersect in P and Q. A chord APB is drawn through P parallel to the line joining the centres O and H and meeting the circles in A and B. From O and H perpendiculars OX and HY are drawn to AB.

a. Prove OH = XY. What is true about OH and AB?

b. Prove OX = HY and also that the chords AP and PB are equal.

Thanks!








































 

kurt.physics

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I'm going to go against my word but that's only because I really need help with Circle Geometry...

Anyway:

AB and DC are chords of a circle which meet when produced at X. The centre of the circle is O. If angleAOB = 110, angleXBC = 68 and angleXCB = 80, find angleCOD.

Thanks!
















 

taggs-sasuke

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I understand why AB is twice the size of OH but how does that make XOHY a rectangle?
 

kurt.physics

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Can I have another clue?

I've found more numbers. ( :) )
For angle x, you must use the fact that the angle at the centre of a circle is twice the angle at the circumference.

So the angle opposite x is 140, so the angle at the centre is 360 - 140 = 220. So 2x = 220, so x = 110

The angle sum of a quadrilateral is 360, so

y + 140 + 110 + 62 = 360

y + 312 = 360

y = 48
 

taggs-sasuke

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For angle x, you must use the fact that the angle at the centre of a circle is twice the angle at the circumference.

So the angle opposite x is 140, so the angle at the centre is 360 - 140 = 220. So 2x = 220, so x = 110

The angle sum of a quadrilateral is 360, so

y + 140 + 110 + 62 = 360

y + 312 = 360

y = 48
Oh...

Thanks.
 

taggs-sasuke

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Quick question:

x = black dot
y = red dot

... but what reason/theorem is it?

(Is it 'opposite angles of a cyclic quadrilateral are supplementary'? But is it a cyclic quadrilateral?)

Thanks!
 

kurt.physics

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Quick question:

x = black dot
y = red dot

... but what reason/theorem is it?

(Is it 'opposite angles of a cyclic quadrilateral are supplementary'? But is it a cyclic quadrilateral?)

Thanks!
Is there any more information?
 

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