Question

what is the answer for the given question could anyone pls answer it​

Answer 1

Answer:

CF=6 unit

Step-by-step explanation:

Given that :

AD: BD=5:3 , BE:EC=3:2 and AC=21

Let CF=x

Then FA=21-x

Using Ceva's theorem

$\frac{AD}{BD} \times \frac{BE}{EC} \times \frac{CF}{FA} =1\\\\ \Rightarrow \frac53 \times \frac32 \times\frac{x}{21-x} =1\\\\ \Rightarrow\frac{15x}{6(21-x)} =1\\\\ \Rightarrow 15x=6(21-x)\\\\ \Rightarrow15x=126-6x\\\\ \Rightarrow 15x+6x=126\\\\ \Rightarrow21x =126\\\\ \Rightarrow x=\frac{126}{21}\\\\ \Rightarrow x=6\\\\ \Rightarrow CF=6 \ unit$