Evaluate CX/AZ

Level 2

In $\triangle ABC$ , $X$ , $Y$ , and $Z$ are points on $BC$ , $CA$ , and $AB$ respectively which $AX$ , $BY$ , and $CZ$ intersects at $O$ . If $AY = 3BX$ and $2BZ = CY$ , evaluate $\dfrac{CX}{AZ}$ .

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\frac{1}{3}

\frac{3}{2}

\frac{2}{3}

1 solution

Tan Peng
Aug 30, 2018

Since the three cevians intersect at one point we an use Ceva's theorem
By Ceva's theorem $\frac{[CY \times AZ \times BX]}{[YA \times BZ \times XC]}$ =1
Since $2BZ = CY$ and $AY = 3BX$
We can simplify to $\frac{2 AZ}{3 CX}$ =1
Therefore $\frac{2}{3}$ = $\frac{CX}{AZ}$

Evaluate CX/AZ

1 solution

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