Math Is Fun Forum

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

On the same straight line there cannot be constructed two similar and

So, according to this figure :http://aleph0.clarku.edu/~djoyce/java/e … III23.html

We cannot have similar segments of circles and unequal ones be built on the same side of the same straight line.

My question is : Can we build similar segments of circles but unequal ones ? (It seems to imply it)

The definition of similar segments of circles is : "Similar segments of circles are those which admit equal angles, or in which the angles equal one another."

Here is the link for it : http://aleph0.clarku.edu/~djoyce/java/e … III11.html

Thank you!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: On the same straight line there cannot be constructed two similar and

EDITED VERSION.

You have a chord and similar segments but on opposite sides of the chord.

Let the chord be AB and choose points C and D, on the circumference, one for each segment.

I'm not sure what is meant by 'similar' here.   If it means that the two segments are the same shape then:

Then, if segment ACB is similar to segment ADB, they must be semi-circles, and angle ACB = ADB = 90.

If it means they are segments made by the same chord then ACBD is a cyclic quadrilateral so ACB + ADB = 180.

Bob

Last edited by Bob (2015-06-19 20:59:53)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: On the same straight line there cannot be constructed two similar and

EDITED VERSION.

You have a chord and similar segments but on opposite sides of the chord.

Let the chord be AB and choose points C and D, on the circumference, one for each segment.

I'm not sure what is meant by 'similar' here.   If it means that the two segments are the same shape then:

Then, if segment ACB is similar to segment ADB, they must be semi-circles, and angle ACB = ADB = 90.

If it means they are segments made by the same chord then ACBD is a cyclic quadrilateral so ACB + ADB = 180.

Bob

Well, from the definition, similar just means that you have equal angles in the segments. If this is the case, we say the segments of circles are similar

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: On the same straight line there cannot be constructed two similar and

Ok thanks.  In which case go back to what I said about cyclic quadrilaterals.  ACBD is cyclic so opposite angles add to 180.  If they are also to be equal then they must both be 90 and the segments are semicircles.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob