Math Is Fun Forum

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

What does this mean?

Prove that the intercept of a tangent between two parallel tangents to a circle subtend 90 Degree at the center.

I think I can prove this but can anyone draw the diagram?

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: What does this mean?

hi Agnishom,

I think this is the diagram.  Circle centre, C.  A, B and D are points on the circumference.

AE and  BF are parallel  tangents and EDF is another tangent (at D) intersecting the other two at E and at F.

Prove that angle ECF = 90.

Hope that's right; over to you to prove it.   

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

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Re: What does this mean?

Thats correct.

But what does intercept mean?

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: What does this mean?

It just means where they cross.  Why some mathematicians use intercept when they could equally use intersection I don't know.  Looking at dictionary.com it seems that an intercept is a line segment made by an intersection, so I suppose it works as the question means the angle made by EF at the centre.  I may just have learnt something there.

But the purpose of the question is surely to test your ability with geometry not your vocabulary.  I prefer to go for simple words whenever possible, so the student is not held up by the language.

true story: Many years ago the maths syllabus I was teaching required students to be able to draw a cumulative frequency graph.

http://www.mathsisfun.com/data/cumulati … raphs.html

The examiner wrote a question asking for an ogive.  All over the country candidates were stumped and so were most of their teachers (me included).  Well it's the same as a cumulative frequency graph; just an old fashioned word for it.  There was a big scandal about it and the exam board had to discount that question in assessing grades.  Since then, papers are always checked by a third party to make sure the words used on the paper are the ones in the syllabus.

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

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

Re: What does this mean?

Why some mathematicians use intercept when they could equally use intersection I don't know.

Do you remember this one?

By the way, the word Ogive is taught over here. Most of my classmates do not know what a 'cumulative frequency' graph is instead.

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.