Question

In the given figure, if AC : CB = 5 : 3, then

• A. $m=5,n=8$
• B. $m=5,n=3$
• C. $m=3,n=5$
• D. $m=3,n=3$

Answer 1

The correct option is B $m=5,n=3$

Given: AC : CB = 5 : 3


Here, ray AX and BY are constructed such that AX || BY and AB is transversal.

In $\Delta A{A}_{m}Cand\Delta B{B}_{n}C$,
$\angle CA{A}_m=\angle CB{B}_n$
(Alternate interior angles)
$\angle C{A}_{m}A=\angle C{B}_{n}B$
(Alternate interior angles)
$\Rightarrow \Delta A{A}_{m}C\sim \Delta B{B}_{n}C$
(By AA similarity)

$\Rightarrow \frac{A{A}_m}{B{B}_n}=\frac{AC}{BC}=\frac{5}{3}$ (Given)

$\Rightarrow A{A}_m:B{B}_n=5:3$

$\Rightarrow m=5andn=3$
Hence, the correct answer is option b.