# [SOLVED] Finding diameter of a cone

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• May 21st 2006, 11:27 AM
Blain
[SOLVED] Finding diameter of a cone
I have a sphere at origin and a known 3d point outside the sphere.
How do I calc the diameter of the cone created by the 3d point
and it's intersection with the sphere (if that makes sense)

Thanks
• May 21st 2006, 12:13 PM
earboth
Quote:

Originally Posted by Blain
I have a sphere at origin and a known 3d point outside the sphere.
How do I calc the diameter of the cone created by the 3d point
and it's intersection with the sphere (if that makes sense)

Thanks

Hello,

I've attached a diagram to show you what I've calculated.

All lines PT form a cone. C is the centre of the sphere. All triangles CTP are right triangles. So the diametre of the cone's base is 2 times the height in the right triangle. The height in a right triangle (and only there) can be calculated by:
$h={{r \cdot TP}\over CP}$

If you know the length of the three lines you only have to plug in the values and caculate the radius of the base.

Greetings

EB
• May 21st 2006, 09:45 PM
earboth
Quote:

Originally Posted by Blain
I have a sphere at origin and a known 3d point outside the sphere.
How do I calc the diameter of the cone created by the 3d point
and it's intersection with the sphere (if that makes sense)

Thanks

Hello,

it's me again:
I've attached a picture which shows sphere and cone from outer space. May be this will help to understand my previous diagram.

Greetings

EB