Question

In a given figure, express X in terms of a, b, c

Answer 1

X=ac/b+c as both small one and the big triangle are similar

Answer 2

In the given figure,

There are two triangle. They are traingle MLN and triangle OPN.

$In \: \triangle \:MLN \: and \: \triangle \: OPN$

$\angle \: LMN \: = \angle \: PON = 64 \degree$

$\angle \: MNL \: = \angle \: PNO = common$

By AA similarity criteria

$\triangle \:MLN \: \sim \: \triangle \: OPN$

So,

$\frac{ON}{MN} = \frac{OP}{LM} \: (cpst)$

$\frac{c}{b + c} = \frac{x}{a}$

$x = \frac{c \times a}{b + c}$