Question

ajutati maaaa ex 10 va rog​

Answer 1

Explicație pas cu pas:

AP este bisectoare =>

$\dfrac{AB}{PB} = \dfrac{AD}{PD} \iff \dfrac{AB}{AD} = \dfrac{PB}{PD} \\ \implies \dfrac{12}{15} = \dfrac{PB}{PD} \iff \dfrac{PB}{PD} = \dfrac{4}{5}$

AQ este bisectoare =>

$\dfrac{AC}{QC} = \dfrac{AD}{QD} \iff \dfrac{AC}{AD} = \dfrac{QC}{QD} \\ \implies \dfrac{12}{15} = \dfrac{QC}{QD} \iff \dfrac{QC}{QD} = \dfrac{4}{5}$

atunci:

$\dfrac{PB}{PD} = \dfrac{QC}{QD} = \dfrac{TA}{TD} = \dfrac{4}{5}$

$\implies (PTQ) \mid\mid (ABC)$

q.e.d.