perplexus.info :: Geometry : External and internal tangents

External and internal tangents (Posted on 2024-11-08)

Consider two circles of different sizes that do not intersect. The smaller circle has center O. Label the intersection of their common external tangents P. A common internal tangent intersects the common external tangents at points A and B. Given that the radius of the larger circle is 11, PO=3, and AB=20√2, find the area of triangle PBA.

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

Comment 2 of 2 |

https://www.desmos.com/calculator/s5ioj6udtm

I solved using Desmos Graphing so detailed formulas are in the link.

Letting the larger circle center at the origin, and P be a sliding point (p,0), I was able to find a formula for AB

AB=(p-3)sqrt(p^2-121)/p

From which p=33

and the area 22sqrt(2)

Posted by Jer on 2024-11-13 07:41:29

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