Question

(Cevas's Theorem) ABC is a triangle and AX, BY and CZ are three concurrent cevians. Then prove:

$\frac{BX}{XC}\cdot \frac{CY}{YA}\cdot \frac{AZ}{ZB}=1$

Answer 1

Given triangle ABC AX, BY and CZ are three concurrent cevians.

Then X ,Y and Z are mid point of AB, BC and AC

Then $AY=CY=\frac{1}{2}AB,$ $AZ=BZ=\frac{1}{2}AC,$ $CX=BX=\frac{1}{2}BC$

$\therefore \frac{BX}{CX}=\frac{AY}{CY}=\frac{AZ}{BZ}=1$