circle

niharika_kumar · 2015-03-04 18:56:29

If two distinct chords of a circle

drawn from a point (p,q) is bisected by x-axis ,then which of the following is correct.

a)

b)
c)
d)

Bob · 2015-03-04 20:48:33

hi Nikarita,

EDIT: See next two posts. New diagram in preparation.

Bob

Last edited by Bob (2015-03-04 21:08:11)

bobbym · 2015-03-04 21:02:15

Hi Bob;

Should (p,q) be on the circle?

Bob · 2015-03-04 21:07:30

Yes it should. Just realised that myself.

New diagram:

Here the centre is now G. A is still (p,q). Chords are BA and CA. Midpoints E and D respectively. F is the origin.

A and F lie on the circle (and B and C of course!)

Haven't got a method yet, but here's a suggestion:

Introduce letters for the coordinates of B and C.

Work out the coordinates of E and D.

Set their y coordinates to zero and see what happens.

More later.

Bob

Olinguito · 2015-03-04 21:22:36

Let A be the point (p,q). The circle is

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[*]

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Clearly the circle passes through the origin O and the point A and has radius OA/2. Thus OA is the diameter the circle.

Because of symmetry we can assume WLOG that p, q > 0 (i.e. A is in the first quadrant). Let a chord drawn from A intersect the x-axis at (t,0). One end of the chord is A; if the axis bisects it, the other end would be (P,Q) where:

[list=1]
[*]

[/*]
[*][/*]
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Susbstiting (x,y) = (P,Q) into the equation of the circle and simplifying gives the following quadratic equation in t:

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[*]

[/*]
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This equation has two real and distinct solutions in t; therefore its discriminant is strictly positive:

[list=*]
[*]

[/*]
[/list]

Last edited by Olinguito (2015-03-04 21:40:50)

Olinguito · 2015-03-04 21:23:41

Do I get a medal for solving this tough problem?

Bob · 2015-03-04 21:47:19

hi Olinguito

I'm considering the medal but you may have to do a little more to satisfy my limited brain .

As my diagram doesn't have OA as diameter, I'm thinking yours is different to mine. Are you able to post a diagram please?

Bob

Olinguito · 2015-03-04 22:05:02

Why doesn't your diagram have OA as diameter? The equation of the circle is

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[*]

[/*]
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which can be rearranged as

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[*]

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which is a circle centred on = midpoint of OA with radius .

Does not that make OA the diameter?

Last edited by Olinguito (2015-03-04 22:28:48)

Bob · 2015-03-04 22:32:06

Why? Because I didn't spot that property. Whoops!

I have a diagram. Now I'm happy.

Medal awarded.

Bob

Olinguito · 2015-03-04 23:11:00

Thanks Bob!

niharika_kumar · 2015-03-05 15:13:55

thanks.

and
HAPPY HOLI to all of you.

niharika_kumar · 2015-03-05 15:15:11

can you give me a diagram of the double ordinate of a parabola.
I am not able to visualize it.

Bob · 2015-03-06 21:36:09

hi Nikarita

I'm not sure what you mean. Quadratic graphs are parabolas and if you draw a line like y = 5, it will usually cut the graph in two places. Have a look at this:

http://www.mathsisfun.com/data/function … 1=x^2-5x+3

You'll have to enter the line yourself. I cannot find the right syntax to put in the link above directly.

Bob

Math Is Fun Forum

#1 2015-03-04 18:56:29

circle

#2 2015-03-04 20:48:33

Re: circle

#3 2015-03-04 21:02:15

Re: circle

#4 2015-03-04 21:07:30

Re: circle

#5 2015-03-04 21:22:36

Re: circle

#6 2015-03-04 21:23:41

Re: circle

#7 2015-03-04 21:47:19

Re: circle

#8 2015-03-04 22:05:02

Re: circle

#9 2015-03-04 22:32:06

Re: circle

#10 2015-03-04 23:11:00

Re: circle

#11 2015-03-05 15:13:55

Re: circle

#12 2015-03-05 15:15:11

Re: circle

#13 2015-03-06 21:36:09

Re: circle

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