Locus of P

Refer to the image. There are circles centred at A, B, C. We create P so that there is a circle centred at P tangent externally to the other 3 circles. Given that the radii of the circles A, B, C can vary, find the locus of P.

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Is the radius of the circle about P fixed? Otherwise, you can pretty much draw 4 circles that satisfy the problem for any position of P.

Gabriel Wong - 8 years ago

What if the circles centered about A, B, C didn't intersect?

Clarence Chew - 8 years ago

P is rights now a point as i see it.. points have no locus.

Rohan Punshi - 8 years ago

"Given that the radii of the circles A, B, C can vary"

Kenneth Chan - 8 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$