Apply Ceva's theorem and find the value of $y$ .

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Solution

The correct option is C 50
Applying Ceva's theorem, $\frac{A F}{F B} . \frac{B D}{D C} . \frac{C E}{E A} = 1$
$\Rightarrow \frac{A F}{F B} . \frac{B D}{D C} . \frac{C E}{E A} = 1$ $\Rightarrow \frac{y}{10} . \frac{15}{45} . \frac{60}{100} = 1$
$\Rightarrow \frac{y}{50} = 1$ $\Rightarrow y = 50$

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x

A F

\frac{A F}{X} . \frac{B D}{D C} . \frac{C E}{E A} = 1

\frac{A F}{F B} . \frac{X}{D C} . \frac{C E}{E A} = 1

\frac{A F}{F B} . \frac{B D}{D C} . \frac{X}{E A} = 1

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