In ΔABC, D is a point on side BC such that ∠ADC = ∠BAC. If CA = 12 cm, CD = 8 cm, then CB (in cm) = ?

Answer: Option A

In ΔABC,
∠BAC = ∠ADC, (given)
In, ΔABC & ΔADC,
∠BAC = ∠ADC (given)
∠C = ∠C (common)
$$\begin{array}{rl}& \therefore \Delta \text{ABC}\sim \Delta \text{DAC}\left(\text{A}-\text{A}\text{theorem}\right)\\ & \frac{\text{BC}}{\text{AC}}=\frac{\text{AC}}{\text{DC}}\\ & \Rightarrow \frac{\text{BC}}{12}=\frac{12}{8}\\ & \Rightarrow \text{BC}=\frac{144}{8}=18\text{ cm}\end{array}$$