Can anyone give me the low down on Ceva's Theorem?

[tamintl]

Hi all,

Can anyone give a quick few lines on what Ceva's theorem consists of?


For example,

'Let ABC be a traingle and suppose there is a circle inside the triangle which is tangent to all three sides. Let it be tangent to BC at P and tangent to CA at Q, and tangent to AB at R.
--> How could i use Ceva's theorem to show that AP, BQ, and CR are concurrent?'

Im not looking for a proof. Just the steps i should take. Any help would be appreciated!

Regards
Tam

 

[Eynstone]

One needs to calculate the ratios BQ/QC &c. & show that the product is 1. The angular version of Ceva's theorem is often easier to use.