Question

Very tough question solve if u can

Answer 1

HOLA

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$ab \: || \: de \: \: ( \: in \: triangle \: abc \: ) \\ \\ \frac{cd}{da } = \: \frac{ce}{eb} \\ \\ bd \: || \: ef \: ( \: in \: triangle \: cdb \: ) \\ \\ \frac{cf}{fd} = \: \frac{ce}{eb} \\ \\ from \: both \: triangles \: we \: get \\ \\ \frac{dc}{da} = \: \frac{ce}{cf} \\ \\ \frac{da}{dc} = \: \frac{cf}{ce} \\ \\ \frac{da}{dc} + \: 1 \: = \: \frac{cf}{ce} + \: 1 \\ \\ \frac{da \: + \: dc}{dc} = \: \frac{cf \: + \: ce}{ce} \\ \\ \\ \frac{ac}{dc} = \: \frac{dc}{cf} \\ \\ dc {}^{2} = \: ac \: \times \: cf$
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