Question

Prove AC : BC - 2: 1​

Answer 1

Step-by-step explanation:

$\rm \large \underline{Given} :-$

$\rm ∠ PAC = \angle QBC = 90^{\circ}$

$\rm AP = 4 \: cm$

$\rm BQ = 2 \: cm$

$\rm \large \underline{To \: Prove } :-$

$\rm AC:CB =2:1$

$\rm \large \underline{Solution}:-$

It is given that,

$\rm ∠ PAC = \angle QBC = 90^{\circ}$

So, by AA similarity ∆PAC ∼ ∆BCQ

Therefore,

$\rm \dfrac{AP}{BQ} = \dfrac{AC}{CB}$

$\rm \dfrac{AC}{CB} = \dfrac{4}{2}$

$\rm \dfrac{AC}{CB} = \dfrac{2}{1}$

$\rm AC:CB = 2:1$