Circles touching internally? (1 Viewer)

Ikki · Jul 16, 2013

I have no idea what it means, but basically the question had two centers and radius's for two circles and told you to justify that the two circles touch internally but when you draw it, one circle is inside the other and then the next part of the questions says to find the point of contact?!

braintic · Jul 16, 2013

Ikki said:
I have no idea what it means, but basically the question had two centers and radius's for two circles and told you to justify that the two circles touch internally but when you draw it, one circle is inside the other and then the next part of the questions says to find the point of contact?!

Could you quote the question.

Kurosaki · Jul 16, 2013

Ikki said:
I have no idea what it means, but basically the question had two centers and radius's for two circles and told you to justify that the two circles touch internally but when you draw it, one circle is inside the other and then the next part of the questions says to find the point of contact?!

If it touches internally, then doesn't that mean that one circle is inside the other and touches the outer circle at one point along its circumference? (I'm probably wrong)

Ikki · Jul 16, 2013

braintic said:
Could you quote the question.

It went something like this.
Two circles with centres (2,1), (3,2) and radii 2,5 respectively touch internally.
A) Justify how they touch internally.
B) Find the point of contact.

Ikki · Jul 16, 2013

Kurosaki said:
If it touches internally, then doesn't that mean that one circle is inside the other and touches the outer circle at one point along its circumference? (I'm probably wrong)

Haha that's the thing, it doesn't, it's a circle inside the other, that's the weird part 0.0

Ikki · Jul 17, 2013

Anyone?

SpiralFlex · Jul 17, 2013

$Two circles are said to have touched each other internally, if the distance from their centres is equal to the difference of their radii.$

$I have drawn two circles: A purple circle and a light blue circle.$

$$Let the purple circle have a radius of$\; R_{1}\; $and the light blue circle have a radius of$\; R_{2}. \;$So according to our statement above, two circles are said to have internally touched if the distance from their centres is equal to the difference in radii. That is, distance from centre$\; = R_{2}-R_{1}.\; $Let's examine if this is the case. Well I have drawn three centre lines. A red line, an orange line and a wax coloured line. We are interested in the wax + orange coloured line because this is the distance we are trying to find (distance from their centres). Now, the red line has a length of$\; R_{1}.\; $We noticed that since, the red line, orange line and wax line have a combined length of$\; R_{2}.\; $The orange and wax line must equal to the length of the combined lines minus the red line. That is,$\; R_{2}-R_{1}$

Ikki · Jul 17, 2013

SpiralFlex said:
$Two circles are said to have touched each other internally, if the distance from their centres is equal to the difference of their radii.$

$I have drawn two circles: A purple circle and a light blue circle.$

$$Let the purple circle have a radius of$\; R_{1}\; $and the light blue circle have a radius of$\; R_{2}. \;$So according to our statement above, two circles are said to have internally touched if the distance from their centres is equal to the difference in radii. That is, distance from centre$\; = R_{2}-R_{1}.\; $Let's examine if this is the case. Well I have drawn three centre lines. A red line, an orange line and a wax coloured line. We are interested in the wax + orange coloured line because this is the distance we are trying to find (distance from their centres). Now, the red line has a length of$\; R_{1}.\; $We noticed that since, the red line, orange line and wax line have a combined length of$\; R_{2}.\; $The orange and wax line must equal to the length of the combined lines minus the red line. That is,$\; R_{2}-R_{1}$

Thanks spiral!!!!

Circles touching internally? (1 Viewer)

Ikki

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braintic

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Kurosaki

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Ikki

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Ikki

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Ikki

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SpiralFlex

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Ikki

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