Math Is Fun Forum

thedarktiger

Member

Registered: 2014-01-10

Posts: 91

power of a point

Let \overline{BC} and \overline{DE} be chords of a circle, which intersect at A, as shown. If AB = 3, BC = 15, and DE = 3, then find AE.

This ones bugging me. how to get it? Its not 18, is it?

thanks!

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: power of a point

hi thedarktiger,

Oh I had a moment of fear at tackling another of these.  I don't see a diagram either but I've made one below.

If that's correct then AE < 3, so not 18.

If you look at triangles ABD and AEC

the angles at A are the same (vertically opposite) and

CBD = CED (angles subtended by the same chord CD)

So those triangles are similar therefore

AB/AD = AE/AC

So let AE = x, and solve for x.

LATER EDIT:

Maybe A is outside the circle ?

You can still find similar triangles:  ADC and ABE.  Different answer but still not 18.
Bob

Last edited by Bob (2014-02-13 02:18:20)

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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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: power of a point

Hi Bob

The equation for x I am getting does not have a solution.

EDIT: When the chords intersect outside the circle I get the answers x=3/5 and x=18/5.

Last edited by anonimnystefy (2014-02-13 14:54:08)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: power of a point

hi Stefy,

Hmmm.  Didn't notice that.  Thanks.  Sketchpad confirmed.

So plan B.  Diagram below.

Show ADC and ABE are similar and work from there.  Different ratio to above post.  I'm not getting those numbers. Mine work in Sketchpad. (My diagram is accurate)

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: power of a point

Hi Bob

You're welcome.

For the case in your diagram I get 18/5.

By the way, shouldn't it be "My work"?

Last edited by anonimnystefy (2014-02-14 02:06:25)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: power of a point

shouldn't it be "My work"?

Didn't I mention that you can dig for coal using Sketchpad ?

I didn't get 18/5 though.  ??

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

thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Re: power of a point

hmm. looks like the answer is not 3 or 18/5 or 3/5 for some reason.
@bob, I know what you mean in your first post.
I really hate these ><

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Good. You can read.

thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Re: power of a point

Hey I got it its 9!!!!!!!!!!
wow I was dumb.
if x = AD then we get the equation
x^2+3x-54 = 0
then factors to (x-6)(x+9) = 0
and x = 6

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Good. You can read.

thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Re: power of a point

and x+3 = 9

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Good. You can read.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: power of a point

Great!  That's what I got! 

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