Question

In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point on AC, such that AP = 6 cm, then find the length of BP.

• A. BP = 4 cm
• B. BP = 8 cm
• C. BP = 6 cm
• D. BP = 12 cm

Answer 1

Answer: (A)

BP = 4 cm

Given that, in $△ABC$, $AB=AC=8cm$, $BC=4cm$ and $AP=6cm$
In $△ABC$,
$\frac{AB}{BC}=\frac{8}{4}=2....\left(i\right)$

$AC=8cm\text{and}AP=6cm$

$\therefore CP=8-6=2cm$

In $\Delta BPC$,
$\frac{BC}{CP}=\frac{4}{2}=2....\left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$, we get:
$\frac{AB}{BC}=\frac{BC}{CP}=2$

Also, angle $C$ is common in both triangles

$\therefore \angle ACB=\angle PCB$

Therefore, by SAS similarity criterion, $\Delta ABC\sim \Delta BPC$
Hence, $\frac{AB}{BP}=\frac{AC}{BC}$

$\frac{8}{BP}=\frac{8}{4}$

$\therefore BP=4cm$